Operators versus Values and Mathematicians' Dysfunction

[Timothy Golden]

When operators came to be embedded into numbers then mathematics lost integrity. The two terms are distinct; the value being a stable thing and the operator an action which generates another value (usually) perhaps from one value or possibly several. But of course mathematics did not evolve with these terms of distinction. Mathematics has accumulated over millennia and does attempt still to abide the accumulation regardless of detected ambiguity.

The theory of types laid out be Russell is already argued as optional within his introduction to the subject. Not so of our modern compiler level languages. His types and the computer types seem to be rather different, yet is the underlying concept the same? His notation honestly was terrible; reusing symbols for ideas that are distinct is what? A typesetter's problem? Whatever; the idea of a strict and structured system has been a theme of mathematics yet the judges are human, and the accumulation is daunting. Simplicity could be had in admitting that operators and values are distinct concepts, and that when operators are embedded within the construction of numbers then such an ambiguity ought at least to go discussed rather than ignored. It is thus not only with irrational values but with rational values as well. The real number menagerie has no universal stature. As a type it is a composition of multiple types upheld as a single type with religiosity... and at this point for any to challenge the standing analysis is suicidal within the arena of mathematical drama.

The falsification in short can be stated simply: A construction of a numerical representation ought not to depend on an operator that will be defined atop the construction.

A concept that applies to one real value ought to apply to all real values. This theme of universality is what one ought to get religious about.
Epsilon/Delta as universal remains to be accepted. The real number as gray is roughly where we land. This is a rather different interpretation of the continuum.

[FromTheRafters]

It happens that Timothy Golden formulated :

> When operators came to be embedded into numbers then mathematics lost
> integrity.

Yeah, like when two forgot that it is actually one plus one.

Why not simplify nomenclature when possible and leave things like the
two-part complex numbers as they are when we can't figure out how to
simplify them?

[Timothy Golden]

I do have a simplification of the complex numbers. It's P3, and by definition it follows the same rules as P2, which masquerade as your miserable real number, and now I can have an expanse away from the modulo abuses of the past. Much as I am not strict these ideas actually are quite strict, and if stricture is a problem to the mathematician then I can happily distance myself from them. That they operate in a pool whose walls are impassable, whereas I am free to travel over on bridges... sometimes just one stepping stone across a stream... the other side is looking quite tantalizing to me. I have a friend who annoyingly and drunkenly announces in the midst of a heated discussion: "OK, everbody out of the pool!". I have no such call. Merely discussion here, but I do try to twist wrists especially those who cannot stare a simple fact in the face. What are operators? What are values?
Are they distinct?

I agree that the summation operator is far more fundamental than the product, and especially division. Indeed division as fundamental is a fraud.
Therefor the field axioms are a fraud. Division is a reverse operation. It is an inverse. The inverse of the inverse is the original. The original of the original is the original. When you say two and I say: "one, one". Then your myth is busted. You want to dodge modulo concepts? Then dodge them fully, sir.

[Timothy Golden]

I think for those of the rational mindset: your work is already corrupted. You work in a corrupt system. As you reradix and refuse to call it so your own regard for the modulo ten system suffers badly, and this is how it is in modern mathematics. When you utter 'two' do not do it as a shrew. When you utter 'three' let's not forget how you learned. The wheels are already spinning. There is even a clickety clack. When you get to 'nine' not all is fine and if you utter 'ten' without a halt or a click at the least then you are missing out. There is an aleph there; an exception; though not a halt really unless one is sought. Can the zero crossing take such meaning? of course it can. It must do such. Our large numbers which allow such grandiose claims as modern mathematics allows provide us these exceptional behaviors per digit. To throw this away as trash is what the rational value mindset does. You re-radix, sir. You are a reradixer!@ You dirty stinking re-radixer! Why? Because the functionality was already built. The option to treat unity as some digit up along the way is obvious and it is only a matter of extending this preexisting mechanism a bit further with the usage of a decimal point if you like. It is thus that the continuum can be born. It is thus that epsilon/delta can apply to all values!

That the operations under discussion in the above paragraph are already embedded in our numerical representation suggests that we do the maximum with that part of number theory. We do not generally consider them to be algebraic yet they are quite tame much of the time. The increment only system (to some the successor?) works out beautifully in general dimension under polysign. We have great ease in exercising epsilon/delta computations. We simply increment and if improved then refine. If unimproved we return to the prior value. Simplicity is on the side of the digital representation rather than the rational, which still relies upon the digital representation generally. Particularly within the construction phase of a numerical system this is true. Clearly upon encountering division; as an operator that values in the number system can be applied to; then the rational study makes sense. Structural integrity demands this. Whatever dis-satisfaction accrues it will point back to the modulo and radix implementation; just where it should be. When you opt to work in sixths you have engaged modulo six. Possibly here there is an extension: when we think in 6.123s have we engaged in a modulo 6.123 interpretation? Under the awareness that is taking place here the fact is that this re-interprets to a modulo 6123 system, with a unital shift of three. If on the way and in the folds someone were to skip over the modulo three system and base theory on a modulo four system whose obvious modulo two shadow part is embedded should we cry foul?

[Timothy Golden]

On Tuesday, November 2, 2021 at 10:44:08 AM UTC-4, FromTheRafters wrote:

> It happens that Timothy Golden formulated :
> > When operators came to be embedded into numbers then mathematics lost
> > integrity.
> Yeah, like when two forgot that it is actually one plus one.

Is it of interest that in the natural numbers they dodge addition and use the successor?
And as to why they do this: isn't it to avoid the conflict as I've laid it out here?

[FromTheRafters]

After serious thinking Timothy Golden wrote :

> On Tuesday, November 2, 2021 at 10:44:08 AM UTC-4, FromTheRafters wrote:
>> It happens that Timothy Golden formulated :
>>> When operators came to be embedded into numbers then mathematics lost
>>> integrity.
>> Yeah, like when two forgot that it is actually one plus one.
>
> Is it of interest that in the natural numbers they dodge addition and use the
> successor? And as to why they do this: isn't it to avoid the conflict as I've
> laid it out here?

That's not the worst of it, if you start out with the primes then all
composite numbers hide multiplication before we even introduce
addition.

Maybe that is why abstraction is so popular. One, the numeral, is just
hiding the fact that it is actually a polynomial in big sigma notation.

Seriously though, I'm okay with abstraction, things can get messy quick
without it.

[zelos...@gmail.com]

Here we go with your crankery again.

>When operators came to be embedded into numbers then mathematics lost integrity.

Operations are functions, numbers are element in a set. They are different kind of things.

a*b is an element, not 2 elements and an operator. * is the operator, a and b are elements, but a*b is only an element because it is the element you get from the operator.

[Timothy Golden]

As far as I know, the real numbers are not constructed through the usage of the product, but they are constructed with the usage of division, which is the rational value. When an operator is embedded into a value and you treat it as a pure value then ambiguity strikes. The point is that there is a distinction between operators and values. Using your instance if a*b does not result in a singular value c then the operation is likewise suspicious. This would take us over to products such as
a0 + a1 x
of abstract algebra, where x is not a real value, but a0 and a1 are real valued. This is not however the topic here, though in the broader awareness of operator theory this is an outstanding conflict given that abstract algebra has formalized operators. This is an especially pernicious instance. The rational value is far more mild and such a simple instance to understand.
Are operators and values distinct concepts?
Clearly if you answer yes, then the expression
a * b
is a composition of two values and one operator. Since you deny this then I can surmise that your answer is no, and this exposes the lack of regard for structured thought within the fundaments of mathematics. Now for a proof I can simply ask you:
1. Is a an operator or a value?
2. Is * an operator or a value?
3. Is b an operator or a value?
4. Is a*b an operator or a value?
5. Is a*b two values and an operator?
Z, you've never been too impressive in terms of applying simple logic. I assure you that simplicity is to be preferred over complexity; particularly as we deal in fundamentals.

[Timothy Golden]

Well Rafters, I see you fending away from the awareness of operators versus values as distinct concepts.
Isn't it obvious that these are distinct?
Isn't it like nouns and verbs in grammar?
Since when does a sentence take the form of a noun?
As to whom ought to be more strict: the mathematician, or the grammarian?
The mathematician ought to abhor the exception, yet it seems to have turned out rather differently.

[FromTheRafters]

Timothy Golden laid this down on his screen :

> On Wednesday, November 3, 2021 at 8:16:57 PM UTC-4, FromTheRafters wrote:
>> After serious thinking Timothy Golden wrote :
>>> On Tuesday, November 2, 2021 at 10:44:08 AM UTC-4, FromTheRafters wrote:
>>>> It happens that Timothy Golden formulated :
>>>>> When operators came to be embedded into numbers then mathematics lost
>>>>> integrity.
>>>> Yeah, like when two forgot that it is actually one plus one.
>>>
>>> Is it of interest that in the natural numbers they dodge addition and use
>>> the successor? And as to why they do this: isn't it to avoid the conflict
>>> as I've laid it out here?
>> That's not the worst of it, if you start out with the primes then all
>> composite numbers hide multiplication before we even introduce
>> addition.
>>
>> Maybe that is why abstraction is so popular. One, the numeral, is just
>> hiding the fact that it is actually a polynomial in big sigma notation.
>>
>> Seriously though, I'm okay with abstraction, things can get messy quick
>> without it.
> Well Rafters, I see you fending away from the awareness of operators versus
> values as distinct concepts.

Not at all, but I'm okay with having elements adjoined to a set in
order to have closure and group operations on a set. It is easy to see
that in unary, concatenation is addition-like and multiplication is
repeated addition we have need for more symbols if we wish to represent
inverses of these operations and convey meaning in symbols. Sure, they
hide underlying structure, but when that structure is not relevant we
can juggle symbols and interpret results after manipulations are
complete.

> Isn't it obvious that these are distinct?

Of course.

> Isn't it like nouns and verbs in grammar?

Yes, like a computer's opcodes and addresses. Actions and things.
Shapes and rotations.

> Since when does a sentence take the form of a noun?

"Rats!" Hey, that's a famous one.

> As to whom ought to be more strict: the mathematician, or the grammarian?
> The mathematician ought to abhor the exception, yet it seems to have turned
> out rather differently.

It is convenient to not have superfluous details explicity dealt with.
We can talk about permutating a set of three objects without having to
describe the objects' size and shape -- they are all aspects which are
abstracted away.

[zelos...@gmail.com]

>As far as I know, the real numbers are not constructed through the usage of the product

Correct, there are many ways, we got sequences, dedekinds cuts. Almost homomorphisms of integers, etc etc

>but they are constructed with the usage of division, which is the rational value.

False. See previous

Rational numbers are constructed as an ordered pair and we define an operator we call division once we have done that.

But a/b is still an element!

>When an operator is embedded into a value and you treat it as a pure value then ambiguity strikes.

There is no ambiguity in a/b or the likes. It is one element.

>The point is that there is a distinction between operators and values.

Depends on how pedantic you want to be. If you are very, no both are just sets :)
If you are less so, then yes because an element is part of the set that we define operators on.

>Using your instance if a*b does not result in a singular value c then the operation is likewise suspicious.

It is a singular element because by definition, an operator, or any function, can only have one output for any given input.

>This would take us over to products such as
>a0 + a1 x

Here we go again, as I have explained to you, that is notation for (a_0, a_1, 0, 0,...)

Learn it already you crank.

>of abstract algebra, where x is not a real value, but a0 and a1 are real valued.

only in R[x], in Q[x] they are rational numbers :) In Z[x] they are integers. The x is there for historical reasons and the ring of polynomials are constructed using sequences as I have informed you.

>This is not however the topic here, though in the broader awareness of operator theory this is an outstanding conflict given that abstract algebra has formalized operators.

There is no conflict, it is just you being an idiot. Your stupidity does not mean there is a conflict.

>This is an especially pernicious instance. The rational value is far more mild and such a simple instance to understand.
>Are operators and values distinct concepts?

As said, depends on how pedantic you are. In the strictest sense from the set theoretical construction, no, they are all just sets.

>a * b
>is a composition of two values and one operator.

False, it is the element that the operator * gives when a and b are the inputs. c=*(a,b), it is a singular element composed of nothing.

>Since you deny this then I can surmise that your answer is no

You cannot because the reason I reject it is because you are so stupid that you think that notation makes the object in question. * is an operator that takes 2 inputs and gives one output. a and b are elements. a*b=*(a,b)=c is an element within the set that * is defined for.

>and this exposes the lack of regard for structured thought within the fundaments of mathematics.

Nope, this shows that you do not understand mathematics, but what else is new?

>1. Is a an operator or a value?

it is an element within the set

>2. Is * an operator or a value?

it is a binary operation defined on the set

> 3. Is b an operator or a value?

It is an element in the set

>4. Is a*b an operator or a value?

It is an element in the set

>5. Is a*b two values and an operator?

It is an element in the set

>Z, you've never been too impressive in terms of applying simple logic.

Given I am vastely superior to you, I should appear like a star to you :)

>I assure you that simplicity is to be preferred over complexity; particularly as we deal in fundamentals.

Yet you understand NOTHING about the fundamentals of mathematics. Not basic notation, not how functions work, you understand NOTHING.

[Timothy Golden]

Ahhh... This bit 'on the set' is quite relevant. Now, choose the set of real numbers and use an operator known as division.
This operator by your own system is defined on the preexisting set. So are the rational numbers, which use division in their construction, in the set?
It seems that by definition the division operator is already 'in the set' and so cannot be seen as 'on the set'.
Then too, the choice of zero as in a/0 guarantees that the result is not in the set. Likewise the sqare root (sqrt(x)) suffers a similar trouble on negative numbers. Still, the product and the sum do act as you describe. You see, when you construct your set with an operator then your claim here about the operator being defined on the set is not valid. This is the case with the rational numbers. These are critical to the real value as they are the interstices between the integers; they are the first development of the continuum within standard mathematics. I would prefer to go another way and simply label the hundredth integer as unity, thus establishing one hundred interstices and carrying on like that as needed, and of course ten is more fundamental and matches exactly the base ten system that is already in use; we reuse existing number theory. Yes, the units position is a new interpretation and has slightly more structure (aka the decimal point), and computations do take on this extra detail. Claims of perfection of numbers goes away, and epsilon/delta applies to all universally. This then resolves the ambiguity that you are about to face on the rational value as fundamental.

> > 3. Is b an o

[FromTheRafters]

Timothy Golden formulated the question :

> On Friday, November 5, 2021 at 1:21:52 AM UTC-4, zelos...@gmail.com wrote:

>> it is a binary operation defined on the set
>
> Ahhh... This bit 'on the set' is quite relevant. Now, choose the set of real
> numbers and use an operator known as division. This operator by your own
> system is defined on the preexisting set. So are the rational numbers, which
> use division in their construction, in the set?

You could say it was defined on the naturals.

[Serg io]

On 11/2/2021 9:17 AM, Timothy Golden wrote:
> When operators came to be embedded into numbers then mathematics lost integrity.

wrong.

[Timothy Golden]

I would think that it is fair to state that the real numbers are built atop division.
Division as an operation is in the set of real numbers isn't it?
This statement goes in distinction to your own :
2. Division is a binary operation defined on the real numbers.

Because the meaning of the distinction is so directly about nouns (values) and verbs (operators)
it does become appropriate doesn't it to talk about these types distinctly. How blunderous it feels when they then take same meaning.
Will you deny me my own grammar? Is yours so superior? Or is it parallelism? No: I falsify your method here. Yet we upon the same grammatical form. I say your operator is in the set. I say my operator is on the set; outside of it; something which comes later and ought not be confused with the set itself. One is action: the operator. The other is value: the material. Ahhh, here we are bridging into philosophy possibly, this notion of material and by it I do mean the physical: without the material there is no count. Show me one who learns to count without material. Well, you go to material as waves rather quickly to get anything sensible, and so it has occurred. Rather than shall we just say that waves are material and that the prior holds? Yes, I'll take that.

Now when we discuss the concept of a verb the strictness is quite direct and nonsensible verbs no doubt arise, but when a noun is a verb then come special state has been achieved. One of us must be speaking like: "Did you axe the tree down or did you use a saw?" and the other: " "I did saw the tree down." "Well, was your did a dud, or what?" Cunningly back "What I did is done, and what I do is forever." Forever on the record are we here now. If I am so incoherent then why not just come out with a few simple statements of the difference between operators and values? I suppose you could ask: "Can the operator be discussed without the values?", and I might quip: "Can the values be discussed without operators?" and it seems that the latter can hold down to counting. And yet denying counting is like denying material. If you wish to preach an immaterial mathematics then please be my guest. I will stay with material mathematics. Indeed the physicists' way is the material way, and it is that way which I have argued for. The rational value as philosophically pure may be had as a stage, and yet it may as well be absorbed into a previous stage at which point its purity is irrelevant. Indeed its impurity stands amplified under the scrutiny. Claiming that one value is composed of two values is about as foolhardy a construction as I can conceive. The notion of an element, and this in your set theory that you seem to think will strengthen your argument... Honestly I have attempted a cleaner form by dodging the set theory I think. Is 'three' one value or two values or three values? five values? If you like all of these then I have a problem with your thinking. All of those things which are equivalent to three contain operators, and until they are solved there is no three. Should I try
6 + 2 = 3 ?
5 - 4 = 3 ?
1 + 2 = 3 ?
It's pretty clear which side of the equation is simpler. Possibly if you found an even simpler form then you'd be onto an argument. Really, simplicity is on my side so strongly here that I feel entitled to print up all this rhetoric. All the valid formulations of three in the world are quite a plurality and if you'd like to start stating them in a long list I'm pretty sure you could do it here on USENET. That is how uncensored this medium is. I'm pretty sure that if I tried to have this conversation over on stack exchange I'd be halted by the censors. Math as religion there.

The preposition seems a bit much to interject here, but because I am suffering this grammatical appropriateness it has to be said:
"A preposition is a word or group of words used before a noun, pronoun, or noun phrase to show direction, time, place, location, spatial relationships, or to introduce an object. Some examples of prepositions are words like "in," "at," "on," "of," and "to." "
- https://academicguides.waldenu.edu/writingcenter/grammar/prepositions

[Timothy Golden]

Yes: an operator lacking closure. Birthing a new number.
Operators as constructors of values.
Sign is like this too.
I'm not really up for having a sub-sign system though.
To create sign once and do it cleanly is enough for a first go.
Having generalized sign I certainly have no ability to claim them to be real valued components that polysign carry.
I have been cornered into challenging the real number for a long time.
The fundamental nature of the real number does not stand any longer.
It can be dismantled and dissected.
Along the way some tender footing deserves to be reviewed.
Now you tell me how a value such as
1.234
ought to be regarded as two values. Pretty clearly there is just a little dot that makes the difference.
Put a little mustache out front of the one and you'll be into polysign shortly, sportly.

[Serg io]

On 11/5/2021 3:59 PM, Timothy Golden wrote:
> On Friday, November 5, 2021 at 1:03:20 PM UTC-4, Serg io wrote:
>> On 11/2/2021 9:17 AM, Timothy Golden wrote:
>>> When operators came to be embedded into numbers then mathematics lost integrity.
>> wrong.
> I would think that it is fair to state that the real numbers are built atop division.
> Division as an operation is in the set of real numbers isn't it?
> This statement goes in distinction to your own :
> 2. Division is a binary operation defined on the real numbers.

division is a "binary input, unitary output" operation,
a number compressor, two go in, one comes out. 60/10 = 6

but addition is "many in, one out" operation 1+1+1+1+1 = 5

factorization is "one in, many out" 60 = 2 * 5 * 2 * 3

so, where are you going with this ?

>
> Because the meaning of the distinction is so directly about nouns (values) and verbs (operators)
> it does become appropriate doesn't it to talk about these types distinctly. How blunderous it feels when they then take same meaning.
> Will you deny me my own grammar?

not at all, I improve it.

>Is yours so superior?

Yes.

>Or is it parallelism?

Never.

>No: I falsify your method here. Yet we upon the same grammatical form. I say your operator is in the set. I say my operator is on the set; outside of it; something which comes later and ought not be confused with the set itself. One is action: the operator. The other is value: the material. Ahhh, here we are bridging into philosophy possibly, this notion of material and by it I do mean the physical: without the material there is no count. Show me one who learns to count without material. Well, you go to material as waves rather quickly to get anything sensible, and so it has occurred. Rather than shall we just say that waves are material and that the prior holds? Yes, I'll take that.
>
> Now when we discuss the concept of a verb the strictness is quite direct and nonsensible verbs no doubt arise, but when a noun is a verb then come special state has been achieved. One of us must be speaking like: "Did you axe the tree down or did you use a saw?" and the other: " "I did saw the tree down." "Well, was your did a dud, or what?" Cunningly back "What I did is done, and what I do is forever." Forever on the record are we here now. If I am so incoherent then why not just come out with a few simple statements of the difference between operators and values? I suppose you could ask: "Can the operator be discussed without the values?", and I might quip: "Can the values be discussed without operators?" and it seems that the latter can hold down to counting. And yet denying counting is like denying material. If you wish to preach an immaterial mathematics then please be my guest. I will stay with material mathematics. Indeed the physicists' way is the material way, and it is that way which I have argued for. The rational value as philosophically pure may be had as a stage, and yet it may as well be absorbed into a previous stage at which point its purity is irrelevant. Indeed its impurity stands amplified under the scrutiny. Claiming that one value is composed of two values is about as foolhardy a construction as I can conceive. The notion of an element, and this in your set theory that you seem to think will strengthen your argument... Honestly I have attempted a cleaner form by dodging the set theory I think. Is 'three' one value or two values or three values? five values?

I will provide you correct thinking on this at a later time.

If you like all of these then I have a problem with your thinking. All of those things which are equivalent to three contain operators, and until they
are solved there is no three. Should I try
> 6 + 2 = 3 ?
> 5 - 4 = 3 ?
> 1 + 2 = 3 ?
> It's pretty clear which side of the equation is simpler. Possibly if you found an even simpler form then you'd be onto an argument. Really, simplicity is on my side so strongly here that I feel entitled to print up all this rhetoric. All the valid formulations of three in the world are quite a plurality and if you'd like to start stating them in a long list I'm pretty sure you could do it here on USENET. That is how uncensored this medium is. I'm pretty sure that if I tried to have this conversation over on stack exchange I'd be halted by the censors. Math as religion there.
>
> The preposition seems a bit much to interject here, but because I am suffering this grammatical appropriateness it has to be said:
> "A preposition is a word or group of words used before a noun, pronoun, or noun phrase to show direction, time, place, location, spatial relationships, or to introduce an object. Some examples of prepositions are words like "in," "at," "on," "of," and "to." "
> - https://academicguides.waldenu.edu/writingcenter/grammar/prepositions
>
>

that is Engrlish, not math, this is sci.math.

[Timothy Golden]

On Friday, November 5, 2021 at 5:40:33 PM UTC-4, Serg io wrote:
> On 11/5/2021 3:59 PM, Timothy Golden wrote:
> > On Friday, November 5, 2021 at 1:03:20 PM UTC-4, Serg io wrote:
> >> On 11/2/2021 9:17 AM, Timothy Golden wrote:
> >>> When operators came to be embedded into numbers then mathematics lost integrity.
> >> wrong.
> > I would think that it is fair to state that the real numbers are built atop division.
> > Division as an operation is in the set of real numbers isn't it?
> > This statement goes in distinction to your own :
> > 2. Division is a binary operation defined on the real numbers.
> division is a "binary input, unitary output" operation,
> a number compressor, two go in, one comes out. 60/10 = 6
>
> but addition is "many in, one out" operation 1+1+1+1+1 = 5
>
> factorization is "one in, many out" 60 = 2 * 5 * 2 * 3

Pretty sure as division is a reverse operation of the product that a multiple form could exist:
60 / 2 / 5 / 2 / 3 = 1 = ((((60 / 2) / 5) / 2) / 3)
My compiler likes it.
But clearly division (and subtraction) are not commutative, whereas the product is.
The product is the more fundamental operation.
This is born out in abstract algebra.
The fact that a reverse operator is in use in the construction of a number system known as the real numbers is problematic.

Much of this is a sidetrack though. The inability to strike the nail on the head with the hammer here is abysmal.
If the fundamentals are broken then what of the pile? More on this later. More on this in the past. More on this now.
It has to be considered that mathematics tries to play nice historically speaking. It tries to be more like a series of rungs on a ladder, but it does branch and rerung. How much of that structure lays on a faulty branching or footing is troubling if the flaw is found down low. The extraordinary inattention to operator theory as a serious pursuit is born and reborn and yet as it is passed beneath our noses nobody seems to smell a thing. It is not our option to falsify this subject. It is enforced that if you fail to mimic then you fail. I guess I am some sort of matheist. Ah, but I do not wish to throw the whole thing away. I can own that I am a social animal whose behaviors are suspect at a level beneath conscious reasoning.

The grammatical analysis is actually quite striking in its appropriateness. If any should make it to a new grammatical structure its adoption by others will be challenging. If wee humans are lacking a grammatical option by genetic limitation it would explain quite a bit. That this could show in mathematics would be quite a plight. Still, if this were the truth it would be no time to shy away.

The reverse operator known as division as well carries an exception. Sadly this is not the end of it. In higher dimension the quantity of exceptions rises. The field axioms are a false start. The product itself suffers none of this. Sure, information can be destroyed through the product, and so never to be recovered again (the reverse operation) but it were not true that
a * b = c
then it will not be true that
c / a = b , c / b = a .
These latter are more results than they are fundamental constructions. Likewise and nearby is the square root. When
x * x = y
then we know that x is a square root of y. The fancy modified division symbol somehow has come to be adopted as if the expression is a raw value. The treatment of variables and constants and actually concrete values is not actually careful enough in mathematics. Particularly when I can express an ambiguity with concrete values then we are down onto something very fundamental. That the abstraction away to 'a' as a value relaxes some of that tension is not actually helpful. A few more steps along and we see entire branches of mathematics composing properties of objects that are completely lacking instantiable forms. Then when an instance pops up it appears to be so trivial that the complexity of the language becomes suspicious. It is unclear to me how much of mathematics is beyond my ability to absorb or how much of it is not worthy of absorption. So I can only plod along and announce falsifications as I bump into them. This attack on the rational value is a bump that I was not looking for. Yet here it is.

You have failed to own or correct your language of the operator as defined 'on' the set, as if the set pre-exists the operator. You have failed to register the fact that the rational value relies upon division to develop the set of real numbers, which is in contradiction to that first statement in this paragraph. That said, you are putting in a decent effort here, Z. Thank you for holding the establishment line. Best of all this is a very simple concept that we are discussing, so I do believe that the truth can be found. The radix mechanism lives nearby. We adopted it first and its reuse here is very sensible.

[Timothy Golden]

The mathematician as information analyst may be a worthy discussion here. It fits my mantra that the divorced topics and their devorcees are practicing a lie. There is no divorce in a unified system. Unity is what we seek. Unification is correct. All z in polysign can take the Unitized() form. All that is needed is a magnitudinal component out front and we can work all z in general dimension on unit shells. Their character is in their angular behaviors, and now it is possible to claim polysign as a source of orthogonality which naturally unfolds from the preexisting simplex balance. The simplex balance is already in use within standard mathematics however it is not generally regarded as a modulo two system, or more properly a modulo 11 system. I do not mean your decimal eleven here, and I would think that any good information analyst could at least admit this simple detail without scrutiny. Nextly why have they not generalized nor even considered the modulo 111 system? Clearly their brights have not been on. Look at how many of them there are as well... and I a simpleton break into general dimensional algebra merely by this option. Really, you ought to be ashmed of yourself, Z.

[Serg io]

that only makes sense if you use Mod0 math and transcribe using ascii II

[Timothy Golden]

For the signature we've settiled in ASCII @ - + * # & ??? (these ellipsis of the unknown perfect for a budding mathematics)
and this lowest @ symbol is intended to represent zero, and yet a double zero it possibly is. This would depend upon where you put your wrapping position. We have to confess that P16 is not really necessarily a fair depiction given the stricture that is occurring. Thus we can improve our purity by discussing
P1111111111111111
and now you can really count yourself lucky while working in Pn.
There are not actually any subsettings happening here. It's just that the kaleidoscopic rotational results are trouble to our understanding. The complex rings are readily exposed from within polysign:
https://drive.google.com/file/d/1UF1pum8eLOR09jTIpt3GdMZlgxYiH5zR/view?usp=sharing
Oddly too, the embedded P3 rings are definable from a singular vector in Pn. We are spec'ing a plane through a vector due to the powers of that vector in the native space. This is the cause of the effect. That we keep seeing modulo three behaviors in all the superspaces, a bifurcation of the evens and odds and the EP2MU which under a fourth root masquerade as Ep3mu (tense change here; for now I like this better.) Also the pu is another mu within the embedded notation. The finder can filter these out, but the results are arbitrary. Either order may be opted for the sake of the analysis. If some compelling RHS versus LHS system guidance could be found polysign could be corrected to that form, but I'm not aware of any need to trouble over this symmetry. It existed in the complex plane as well.

Forthcoming I'll simply label the graphic above with these coordinates. This could be a substantial graphic to some. It's a nice proof.
Orthogonality arrives here as well. It's only predecessor would be Pn in high n, but these effects are coming out down low. These rings literally dominate under the self product, and really at random, as proven in the above graphic, the overwhelming majority of positions land themselves planar and fairly distributed. As well we are witnessing a magnitudinal growth factor with the signature based on powers of unit vectors out merely to four powers zzzz. It's causing me to go back to
http://bandtechnology.com/PolySigned/MagnitudeAnalysis.html
but the values are not lining up.
There is always the possibility of a bug, and then too that data did nothing about getting onto a ring. The math now is on the rings that is coming to the clean figures. The latest data I guess it at the tail here.


In CheckTheONEs

EMU1: [P4 0.224144, 1.06066, 0.836516, 0 ]
Error: 9.69969e-11
Verified: EMU1^3 == ONE1 == ONE1*ONE1 (unitized)
Nonunitized zzz (EMU) magnitude was 1.5
Nonunitized zz (ONE) magnitude was 1.22474
squared: 1.5
ONE1: [P4 1.22474, 0.612372, 0, 0.612372 ]

Sum of ONEs (EMUs^3): [P4 1.22474, 0.612372, 0, 0.612372 ]


In CheckTheONEs

EMU1: [P5 0.270481, 0, 0.494194, 1.0701, 0.931841 ]
Error: 2.53382e-11
Verified: EMU1^3 == ONE1 == ONE1*ONE1 (unitized)
Nonunitized zzz (EMU) magnitude was 2
Nonunitized zz (ONE) magnitude was 1.41421
squared: 2
ONE1: [P5 1.02333, 0.632456, 0, 1.08624e-12, 0.632456 ]
EMU2: [P5 0.270481, 0.494194, 0.931841, 0, 1.0701 ]
Error: 7.79318e-11
Verified: EMU2^3 == ONE2 == ONE2*ONE2 (unitized)
Nonunitized zzz (EMU) magnitude was 2
Nonunitized zz (ONE) magnitude was 1.41421
squared: 2
ONE2: [P5 1.02333, 1.30795e-11, 0.632456, 0.632456, 0 ]

Sum of ONEs (EMUs^3): [P5 1.41421, 1.6785e-11, 0, 2.22493e-11, 5.46363e-12 ]


In CheckTheONEs

EMU1: [P6 8.19541e-12, 0.790569, 0, 4.48791e-11, 0.790569, 3.66837e-11 ]
Error: 5.10998e-11
Verified: EMU1^3 == ONE1 == ONE1*ONE1 (unitized)
Nonunitized zzz (EMU) magnitude was 2.5
Nonunitized zz (ONE) magnitude was 1.58114
squared: 2.5
ONE1: [P6 0.790569, 0, 2.45862e-11, 0.790569, 0, 2.45862e-11 ]
EMU2: [P6 0.263523, 0.790569, 1.05409, 0.790569, 0.263523, 0 ]
Error: 3.68815e-11
Verified: EMU2^3 == ONE2 == ONE2*ONE2 (unitized)
Nonunitized zzz (EMU) magnitude was 2.5
Nonunitized zz (ONE) magnitude was 1.58114
squared: 2.5
ONE2: [P6 1.05409, 0.790569, 0.263523, 0, 0.263523, 0.790569 ]

Sum of ONEs (EMUs^3): [P6 1.58114, 0.527046, 3.06551e-11, 0.527046, 0, 0.527046 ]


In CheckTheONEs

EMU1: [P7 0.241909, 0, 0.126578, 0.526326, 0.898227, 0.96223, 0.670141 ]
Error: 4.30175e-11
Verified: EMU1^3 == ONE1 == ONE1*ONE1 (unitized)
Nonunitized zzz (EMU) magnitude was 3
Nonunitized zz (ONE) magnitude was 1.73205
squared: 3
ONE1: [P7 0.940736, 0.754411, 0.335745, 3.90576e-12, 0, 0.335745, 0.754411 ]
EMU2: [P7 0.241909, 0.96223, 0.526326, 0, 0.670141, 0.898227, 0.126578 ]
Error: 1.29158e-11
Verified: EMU2^3 == ONE2 == ONE2*ONE2 (unitized)
Nonunitized zzz (EMU) magnitude was 3
Nonunitized zz (ONE) magnitude was 1.73205
squared: 3
ONE2: [P7 0.940736, 0.335745, 0, 0.754411, 0.754411, 7.66054e-14, 0.335745 ]
EMU3: [P7 0.241909, 0.526326, 0.670141, 0.126578, 0.96223, 0, 0.898227 ]
Error: 3.30493e-11
Verified: EMU3^3 == ONE3 == ONE3*ONE3 (unitized)
Nonunitized zzz (EMU) magnitude was 3
Nonunitized zz (ONE) magnitude was 1.73205
squared: 3
ONE3: [P7 0.940736, 1.23279e-12, 0.754411, 0.335745, 0.335745, 0.754411, 0 ]

Sum of ONEs (EMUs^3): [P7 1.73205, 8.44347e-12, 7.45981e-12, 7.49001e-12, 9.51905e-13, 9.82547e-13, 0 ]


In CheckTheONEs

EMU1: [P8 0.217917, 0.572822, 0.856817, 0.903541, 0.685624, 0.330719, 0.0467241, 0 ]
Error: 5.50984e-11
Verified: EMU1^3 == ONE1 == ONE1*ONE1 (unitized)
Nonunitized zzz (EMU) magnitude was 3.5
Nonunitized zz (ONE) magnitude was 1.87083
squared: 3.5
ONE1: [P8 0.935414, 0.798426, 0.467707, 0.136988, 0, 0.136988, 0.467707, 0.798426 ]
EMU2: [P8 0.171193, 0, 0.6389, 0.810093, 0.171193, 1.14983e-11, 0.6389, 0.810093 ]
Error: 2.36212e-11
Verified: EMU2^3 == ONE2 == ONE2*ONE2 (unitized)
Nonunitized zzz (EMU) magnitude was 3.5
Nonunitized zz (ONE) magnitude was 1.87083
squared: 3.5
ONE2: [P8 0.935414, 0.467707, 0, 0.467707, 0.935414, 0.467707, 0, 0.467707 ]
EMU3: [P8 0.217917, 0.903541, 0.0467241, 0.572822, 0.685624, 0, 0.856817, 0.330719 ]
Error: 7.59919e-11
Verified: EMU3^3 == ONE3 == ONE3*ONE3 (unitized)
Nonunitized zzz (EMU) magnitude was 3.5
Nonunitized zz (ONE) magnitude was 1.87083
squared: 3.5
ONE3: [P8 0.935414, 0.136988, 0.467707, 0.798426, 0, 0.798426, 0.467707, 0.136988 ]

Sum of ONEs (EMUs^3): [P8 1.87083, 0.467707, 9.29101e-12, 0.467707, 4.64528e-12, 0.467707, 0, 0.467707 ]


In CheckTheONEs

EMU1: [P9 4.28772e-11, 0.666667, 8.48234e-11, 1.46027e-11, 0.666667, 5.16988e-25, 1.46027e-11, 0.666667, 0 ]
Error: 7.96494e-11
Verified: EMU1^3 == ONE1 == ONE1*ONE1 (unitized)
Nonunitized zzz (EMU) magnitude was 4
Nonunitized zz (ONE) magnitude was 2
squared: 4
ONE1: [P9 0.666667, 1.27408e-11, 1.29247e-26, 0.666667, 1.27408e-11, 0, 0.666667, 1.27408e-11, 1.29247e-26 ]
EMU2: [P9 0.195419, 0, 3.8191e-12, 0.195419, 0.494818, 0.758105, 0.862086, 0.758105, 0.494818 ]
Error: 3.77875e-11
Verified: EMU2^3 == ONE2 == ONE2*ONE2 (unitized)
Nonunitized zzz (EMU) magnitude was 4
Nonunitized zz (ONE) magnitude was 2
squared: 4
ONE2: [P9 0.862086, 0.758105, 0.494818, 0.195419, 0, 1.08336e-12, 0.195419, 0.494818, 0.758105 ]
EMU3: [P9 0.195419, 0, 0.494818, 0.862086, 0.494818, 2.2852e-12, 0.195419, 0.758105, 0.758105 ]
Error: 1.63751e-11
Verified: EMU3^3 == ONE3 == ONE3*ONE3 (unitized)
Nonunitized zzz (EMU) magnitude was 4
Nonunitized zz (ONE) magnitude was 2
squared: 4
ONE3: [P9 0.862086, 0.494818, 0, 0.195419, 0.758105, 0.758105, 0.195419, 7.45848e-13, 0.494818 ]
EMU4: [P9 0.195419, 0.758105, 0, 0.862086, 3.02225e-12, 0.758105, 0.195419, 0.494818, 0.494818 ]
Error: 6.15443e-11
Verified: EMU4^3 == ONE4 == ONE4*ONE4 (unitized)
Nonunitized zzz (EMU) magnitude was 4
Nonunitized zz (ONE) magnitude was 2
squared: 4
ONE4: [P9 0.862086, 2.85749e-12, 0.758105, 0.195419, 0.494818, 0.494818, 0.195419, 0.758105, 0 ]

Sum of ONEs (EMUs^3): [P9 2, 1.66946e-11, 0, 1.41787e-11, 1.34042e-11, 8.57203e-12, 7.79687e-12, 2.19769e-11, 5.28089e-12 ]


In CheckTheONEs

EMU1: [P10 0.202861, 0.0274084, 0, 0.131105, 0.370645, 0.627125, 0.802577, 0.829986, 0.698881, 0.459341 ]
Error: 6.98756e-11
Verified: EMU1^3 == ONE1 == ONE1*ONE1 (unitized)
Nonunitized zzz (EMU) magnitude was 4.5
Nonunitized zz (ONE) magnitude was 2.12132
squared: 4.5
ONE1: [P10 0.848528, 0.767501, 0.555369, 0.293159, 0.0810272, 0, 0.0810272, 0.293159, 0.555369, 0.767501 ]
EMU2: [P10 0.202861, 0, 0.370645, 0.802577, 0.698881, 0.202861, 0, 0.370645, 0.802577, 0.698881 ]
Error: 4.89003e-11
Verified: EMU2^3 == ONE2 == ONE2*ONE2 (unitized)
Nonunitized zzz (EMU) magnitude was 4.5
Nonunitized zz (ONE) magnitude was 2.12132
squared: 4.5
ONE2: [P10 0.767501, 0.474342, 0, 3.65596e-12, 0.474342, 0.767501, 0.474342, 0, 3.65596e-12, 0.474342 ]
EMU3: [P10 0.202861, 0.370645, 0.698881, 0, 0.802577, 0.202861, 0.370645, 0.698881, 0, 0.802577 ]
Error: 1.8154e-11
Verified: EMU3^3 == ONE3 == ONE3*ONE3 (unitized)
Nonunitized zzz (EMU) magnitude was 4.5
Nonunitized zz (ONE) magnitude was 2.12132
squared: 4.5
ONE3: [P10 0.767501, 0, 0.474342, 0.474342, 7.64189e-12, 0.767501, 0, 0.474342, 0.474342, 7.64189e-12 ]
EMU4: [P10 0.202861, 0.829986, 0.370645, 0.0274084, 0.698881, 0.627125, 0, 0.459341, 0.802577, 0.131105 ]
Error: 7.46484e-11
Verified: EMU4^3 == ONE4 == ONE4*ONE4 (unitized)
Nonunitized zzz (EMU) magnitude was 4.5
Nonunitized zz (ONE) magnitude was 2.12132
squared: 4.5
ONE4: [P10 0.848528, 0.293159, 0.0810272, 0.767501, 0.555369, 0, 0.555369, 0.767501, 0.0810272, 0.293159 ]

Sum of ONEs (EMUs^3): [P10 2.12132, 0.424264, 0, 0.424264, 5.44809e-12, 0.424264, 3.40616e-12, 0.424264, 8.85447e-12, 0.424264 ]


In CheckTheONEs

EMU1: [P11 0.201438, 0.782152, 0.500567, 0, 0.424062, 0.803928, 0.271745, 0.0433539, 0.640544, 0.698957, 0.0851409 ]
Error: 9.61243e-11
Verified: EMU1^3 == ONE1 == ONE1*ONE1 (unitized)
Nonunitized zzz (EMU) magnitude was 5
Nonunitized zz (ONE) magnitude was 2.23607
squared: 5
ONE1: [P11 0.796647, 0.33223, 0, 0.55898, 0.732108, 0.123851, 0.123851, 0.732108, 0.55898, 2.33147e-14, 0.33223 ]
EMU2: [P11 0.201438, 0.0433539, 0, 0.0851409, 0.271745, 0.500567, 0.698957, 0.803928, 0.782152, 0.640544, 0.424062 ]
Error: 8.28956e-11
Verified: EMU2^3 == ONE2 == ONE2*ONE2 (unitized)
Nonunitized zzz (EMU) magnitude was 5
Nonunitized zz (ONE) magnitude was 2.23607
squared: 5
ONE2: [P11 0.796647, 0.732108, 0.55898, 0.33223, 0.123851, 4.71401e-12, 0, 0.123851, 0.33223, 0.55898, 0.732108 ]
EMU3: [P11 0.201438, 0.698957, 0.0433539, 0.803928, 0, 0.782152, 0.0851409, 0.640544, 0.271745, 0.424062, 0.500567 ]
Error: 5.82021e-11
Verified: EMU3^3 == ONE3 == ONE3*ONE3 (unitized)
Nonunitized zzz (EMU) magnitude was 5
Nonunitized zz (ONE) magnitude was 2.23607
squared: 5
ONE3: [P11 0.796647, 1.88272e-12, 0.732108, 0.123851, 0.55898, 0.33223, 0.33223, 0.55898, 0.123851, 0.732108, 0 ]
EMU4: [P11 0.201438, 0, 0.271745, 0.698957, 0.782152, 0.424062, 0.0433539, 0.0851409, 0.500567, 0.803928, 0.640544 ]
Error: 9.89181e-11
Verified: EMU4^3 == ONE4 == ONE4*ONE4 (unitized)
Nonunitized zzz (EMU) magnitude was 5
Nonunitized zz (ONE) magnitude was 2.23607
squared: 5
ONE4: [P11 0.796647, 0.55898, 0.123851, 2.09455e-12, 0.33223, 0.732108, 0.732108, 0.33223, 0, 0.123851, 0.55898 ]
EMU5: [P11 0.201438, 0.803928, 0.0851409, 0.424062, 0.698957, 0, 0.640544, 0.500567, 0.0433539, 0.782152, 0.271745 ]
Error: 2.90418e-11
Verified: EMU5^3 == ONE5 == ONE5*ONE5 (unitized)
Nonunitized zzz (EMU) magnitude was 5
Nonunitized zz (ONE) magnitude was 2.23607
squared: 5
ONE5: [P11 0.796647, 0.123851, 0.33223, 0.732108, 0, 0.55898, 0.55898, 1.09956e-12, 0.732108, 0.33223, 0.123851 ]

Sum of ONEs (EMUs^3): [P11 2.23607, 1.14089e-11, 1.56746e-11, 2.15221e-11, 1.71956e-11, 2.02407e-11, 1.28009e-12, 4.32521e-12, 0, 5.84599e-12, 1.01117e-11 ]


In CheckTheONEs

EMU1: [P12 0.195434, 0.72937, 0, 0.72937, 0.195434, 0.390868, 0.586302, 0.0523664, 0.781736, 0.0523664, 0.586302, 0.390868 ]
Error: 4.2193e-11
Verified: EMU1^3 == ONE1 == ONE1*ONE1 (unitized)
Nonunitized zzz (EMU) magnitude was 5.5
Nonunitized zz (ONE) magnitude was 2.34521
squared: 5.5
ONE1: [P12 0.781736, 0.0523664, 0.586302, 0.390868, 0.195434, 0.72937, 0, 0.72937, 0.195434, 0.390868, 0.586302, 0.0523664 ]
EMU2: [P12 0.195434, 0, 0.195434, 0.586302, 0.781736, 0.586302, 0.195434, 4.68375e-17, 0.195434, 0.586302, 0.781736, 0.586302 ]
Error: 9.64404e-11
Verified: EMU2^3 == ONE2 == ONE2*ONE2 (unitized)
Nonunitized zzz (EMU) magnitude was 5.5
Nonunitized zz (ONE) magnitude was 2.34521
squared: 5.5
ONE2: [P12 0.781736, 0.586302, 0.195434, 0, 0.195434, 0.586302, 0.781736, 0.586302, 0.195434, 0, 0.195434, 0.586302 ]
EMU3: [P12 0.143068, 0.677003, 0.533936, 0, 0.143068, 0.677003, 0.533936, 0, 0.143068, 0.677003, 0.533936, 0 ]
Error: 4.84322e-11
Verified: EMU3^3 == ONE3 == ONE3*ONE3 (unitized)
Nonunitized zzz (EMU) magnitude was 5.5
Nonunitized zz (ONE) magnitude was 2.34521
squared: 5.5
ONE3: [P12 0.781736, 0.390868, 0, 0.390868, 0.781736, 0.390868, 0, 0.390868, 0.781736, 0.390868, 0, 0.390868 ]
EMU4: [P12 3.64121e-11, 4.67191e-12, 0.586302, 0, 1.19543e-11, 0.586302, 0, 4.67191e-12, 0.586302, 0, 1.19543e-11, 0.586302 ]
Error: 3.48024e-11
Verified: EMU4^3 == ONE4 == ONE4*ONE4 (unitized)
Nonunitized zzz (EMU) magnitude was 5.5
Nonunitized zz (ONE) magnitude was 2.34521
squared: 5.5
ONE4: [P12 0.586302, 2.3697e-12, 0, 0.586302, 2.3697e-12, 0, 0.586302, 2.3697e-12, 0, 0.586302, 2.3697e-12, 0 ]
EMU5: [P12 0.195434, 0.0523664, 0, 0.0523664, 0.195434, 0.390868, 0.586302, 0.72937, 0.781736, 0.72937, 0.586302, 0.390868 ]
Error: 6.34729e-11
Verified: EMU5^3 == ONE5 == ONE5*ONE5 (unitized)
Nonunitized zzz (EMU) magnitude was 5.5
Nonunitized zz (ONE) magnitude was 2.34521
squared: 5.5
ONE5: [P12 0.781736, 0.72937, 0.586302, 0.390868, 0.195434, 0.0523664, 0, 0.0523664, 0.195434, 0.390868, 0.586302, 0.72937 ]

Sum of ONEs (EMUs^3): [P12 2.34521, 0.390868, 0, 0.390868, 1.24349e-11, 0.390868, 8.81584e-12, 0.390868, 5.1954e-12, 0.390868, 1.76308e-11, 0.390868 ]


In CheckTheONEs

EMU1: [P13 0.1872, 0.360449, 0.537173, 0.676888, 0.747587, 0.733073, 0.636672, 0.480467, 0.300244, 0.137289, 0.0289333, 0, 0.0571173 ]
Error: 4.37606e-11
Verified: EMU1^3 == ONE1 == ONE1*ONE1 (unitized)
Nonunitized zzz (EMU) magnitude was 6
Nonunitized zz (ONE) magnitude was 2.44949
squared: 6
ONE1: [P13 0.742739, 0.699573, 0.579966, 0.411318, 0.232263, 0.0838219, 0, 6.84786e-13, 0.0838219, 0.232263, 0.411318, 0.579966, 0.699573 ]
EMU2: [P13 0.1872, 0.300244, 0.676888, 0, 0.636672, 0.360449, 0.137289, 0.747587, 0.0571173, 0.480467, 0.537173, 0.0289333, 0.733073 ]
Error: 5.53374e-11
Verified: EMU2^3 == ONE2 == ONE2*ONE2 (unitized)
Nonunitized zzz (EMU) magnitude was 6
Nonunitized zz (ONE) magnitude was 2.44949
squared: 6
ONE2: [P13 0.742739, 0.0838219, 0.411318, 0.579966, 2.3801e-12, 0.699573, 0.232263, 0.232263, 0.699573, 0, 0.579966, 0.411318, 0.0838219 ]
EMU3: [P13 0.1872, 0.636672, 0.0571173, 0.733073, 0, 0.747587, 0.0289333, 0.676888, 0.137289, 0.537173, 0.300244, 0.360449, 0.480467 ]
Error: 3.88203e-11
Verified: EMU3^3 == ONE3 == ONE3*ONE3 (unitized)
Nonunitized zzz (EMU) magnitude was 6
Nonunitized zz (ONE) magnitude was 2.44949
squared: 6
ONE3: [P13 0.742739, 5.32685e-13, 0.699573, 0.0838219, 0.579966, 0.232263, 0.411318, 0.411318, 0.232263, 0.579966, 0.0838219, 0.699573, 0 ]
EMU4: [P13 0.1872, 0, 0.137289, 0.480467, 0.733073, 0.676888, 0.360449, 0.0571173, 0.0289333, 0.300244, 0.636672, 0.747587, 0.537173 ]
Error: 3.14432e-11
Verified: EMU4^3 == ONE4 == ONE4*ONE4 (unitized)
Nonunitized zzz (EMU) magnitude was 6
Nonunitized zz (ONE) magnitude was 2.44949
squared: 6
ONE4: [P13 0.742739, 0.579966, 0.232263, 0, 0.0838219, 0.411318, 0.699573, 0.699573, 0.411318, 0.0838219, 3.63265e-13, 0.232263, 0.579966 ]
EMU5: [P13 0.1872, 0.0289333, 0.480467, 0.747587, 0.360449, 0, 0.300244, 0.733073, 0.537173, 0.0571173, 0.137289, 0.636672, 0.676888 ]
Error: 4.78371e-11
Verified: EMU5^3 == ONE5 == ONE5*ONE5 (unitized)
Nonunitized zzz (EMU) magnitude was 6
Nonunitized zz (ONE) magnitude was 2.44949
squared: 6
ONE5: [P13 0.742739, 0.411318, 0, 0.232263, 0.699573, 0.579966, 0.0838219, 0.0838219, 0.579966, 0.699573, 0.232263, 5.11147e-13, 0.411318 ]
EMU6: [P13 0.1872, 0.747587, 0.300244, 0.0571173, 0.676888, 0.480467, 0, 0.537173, 0.636672, 0.0289333, 0.360449, 0.733073, 0.137289 ]
Error: 2.47023e-11
Verified: EMU6^3 == ONE6 == ONE6*ONE6 (unitized)
Nonunitized zzz (EMU) magnitude was 6
Nonunitized zz (ONE) magnitude was 2.44949
squared: 6
ONE6: [P13 0.742739, 0.232263, 0.0838219, 0.699573, 0.411318, 0, 0.579966, 0.579966, 2.14717e-13, 0.411318, 0.699573, 0.0838219, 0.232263 ]

Sum of ONEs (EMUs^3): [P13 2.44949, 1.8594e-12, 8.8014e-12, 2.65343e-12, 7.20268e-12, 8.9897e-12, 0, 1.36411e-11, 4.65272e-12, 6.44018e-12, 1.09881e-11, 4.84102e-12, 1.17821e-11 ]


In CheckTheONEs

EMU1: [P14 0.17804, 0.227085, 0.708182, 0.0592186, 0.387366, 0.627137, 0, 0.542256, 0.493211, 0.0121131, 0.661077, 0.33293, 0.0931587, 0.720295 ]
Error: 5.49482e-11
Verified: EMU1^3 == ONE1 == ONE1*ONE1 (unitized)
Nonunitized zzz (EMU) magnitude was 6.5
Nonunitized zz (ONE) magnitude was 2.54951
squared: 6.5
ONE1: [P14 0.728431, 0.137131, 0.28317, 0.692363, 0.0360687, 0.445261, 0.5913, 0, 0.5913, 0.445261, 0.0360687, 0.692363, 0.28317, 0.137131 ]
EMU2: [P14 0.17804, 0, 0.0931587, 0.387366, 0.661077, 0.708182, 0.493211, 0.17804, 0, 0.0931587, 0.387366, 0.661077, 0.708182, 0.493211 ]
Error: 5.01628e-11
Verified: EMU2^3 == ONE2 == ONE2*ONE2 (unitized)
Nonunitized zzz (EMU) magnitude was 6.5
Nonunitized zz (ONE) magnitude was 2.54951
squared: 6.5
ONE2: [P14 0.692363, 0.555232, 0.247101, 6.10401e-13, 0, 0.247101, 0.555232, 0.692363, 0.555232, 0.247101, 6.10401e-13, 0, 0.247101, 0.555232 ]
EMU3: [P14 0.17804, 0.387366, 0.493211, 0.0931587, 0.708182, 0, 0.661077, 0.17804, 0.387366, 0.493211, 0.0931587, 0.708182, 0, 0.661077 ]
Error: 6.31541e-11
Verified: EMU3^3 == ONE3 == ONE3*ONE3 (unitized)
Nonunitized zzz (EMU) magnitude was 6.5
Nonunitized zz (ONE) magnitude was 2.54951
squared: 6.5
ONE3: [P14 0.692363, 0, 0.555232, 0.247101, 0.247101, 0.555232, 4.4782e-12, 0.692363, 2.22045e-16, 0.555232, 0.247101, 0.247101, 0.555232, 4.4782e-12 ]
EMU4: [P14 0.17804, 0.0121131, 0.387366, 0.720295, 0.493211, 0.0592186, 0.0931587, 0.542256, 0.708182, 0.33293, 0, 0.227085, 0.661077, 0.627137 ]
Error: 6.49721e-11
Verified: EMU4^3 == ONE4 == ONE4*ONE4 (unitized)
Nonunitized zzz (EMU) magnitude was 6.5
Nonunitized zz (ONE) magnitude was 2.54951
squared: 6.5
ONE4: [P14 0.728431, 0.445261, 0.0360687, 0.137131, 0.5913, 0.692363, 0.28317, 0, 0.28317, 0.692363, 0.5913, 0.137131, 0.0360687, 0.445261 ]
EMU5: [P14 0.17804, 0.708182, 0.387366, 0, 0.493211, 0.661077, 0.0931587, 0.17804, 0.708182, 0.387366, 0, 0.493211, 0.661077, 0.0931587 ]
Error: 9.69908e-11
Verified: EMU5^3 == ONE5 == ONE5*ONE5 (unitized)
Nonunitized zzz (EMU) magnitude was 6.5
Nonunitized zz (ONE) magnitude was 2.54951
squared: 6.5
ONE5: [P14 0.692363, 0.247101, 5.79581e-12, 0.555232, 0.555232, 0, 0.247101, 0.692363, 0.247101, 5.79603e-12, 0.555232, 0.555232, 2.22045e-16, 0.247101 ]
EMU6: [P14 0.17804, 0.33293, 0.493211, 0.627137, 0.708182, 0.720295, 0.661077, 0.542256, 0.387366, 0.227085, 0.0931587, 0.0121131, 0, 0.0592186 ]
Error: 7.42616e-11
Verified: EMU6^3 == ONE6 == ONE6*ONE6 (unitized)
Nonunitized zzz (EMU) magnitude was 6.5
Nonunitized zz (ONE) magnitude was 2.54951
squared: 6.5
ONE6: [P14 0.728431, 0.692363, 0.5913, 0.445261, 0.28317, 0.137131, 0.0360687, 0, 0.0360687, 0.137131, 0.28317, 0.445261, 0.5913, 0.692363 ]

Sum of ONEs (EMUs^3): [P14 2.54951, 0.364216, 2.24927e-11, 0.364216, 1.64371e-11, 0.364216, 1.64608e-11, 0.364216, 6.03184e-12, 0.364216, 6.05671e-12, 0.364216, 0, 0.364216 ]


In CheckTheONEs

EMU1: [P15 0.168675, 0.0596637, 0.581105, 0.581105, 0.0596637, 0.168675, 0.667327, 0.454069, 0, 0.308184, 0.697825, 0.308184, 1.08982e-11, 0.454069, 0.667327 ]
Error: 8.10427e-11
Verified: EMU1^3 == ONE1 == ONE1*ONE1 (unitized)
Nonunitized zzz (EMU) magnitude was 7
Nonunitized zz (ONE) magnitude was 2.64575
squared: 7
ONE1: [P15 0.697825, 0.308184, 0, 0.454069, 0.667327, 0.168675, 0.0596637, 0.581105, 0.581105, 0.0596637, 0.168675, 0.667327, 0.454069, 3.64708e-13, 0.308184 ]
EMU2: [P15 0.168675, 0.0596637, 6.16075e-11, 0, 0.0596637, 0.168675, 0.308184, 0.454069, 0.581105, 0.667327, 0.697825, 0.667327, 0.581105, 0.454069, 0.308184 ]
Error: 7.89257e-11
Verified: EMU2^3 == ONE2 == ONE2*ONE2 (unitized)
Nonunitized zzz (EMU) magnitude was 7
Nonunitized zz (ONE) magnitude was 2.64575
squared: 7
ONE2: [P15 0.697825, 0.667327, 0.581105, 0.454069, 0.308184, 0.168675, 0.0596637, 0, 1.23235e-12, 0.0596637, 0.168675, 0.308184, 0.454069, 0.581105, 0.667327 ]
EMU3: [P15 0.168675, 0.308184, 0.581105, 0, 0.667327, 0.168675, 0.308184, 0.581105, 9.81554e-12, 0.667327, 0.168675, 0.308184, 0.581105, 1.99952e-12, 0.667327 ]
Error: 8.78221e-11
Verified: EMU3^3 == ONE3 == ONE3*ONE3 (unitized)
Nonunitized zzz (EMU) magnitude was 7
Nonunitized zz (ONE) magnitude was 2.64575
squared: 7
ONE3: [P15 0.638161, 4.44089e-16, 0.394405, 0.394405, 5.66214e-13, 0.638161, 4.44089e-16, 0.394405, 0.394405, 5.66214e-13, 0.638161, 0, 0.394405, 0.394405, 5.66214e-13 ]
EMU4: [P15 0.168675, 0.581105, 0.667327, 0.308184, 0, 0.168675, 0.581105, 0.667327, 0.308184, 0, 0.168675, 0.581105, 0.667327, 0.308184, 0 ]
Error: 4.62809e-11
Verified: EMU4^3 == ONE4 == ONE4*ONE4 (unitized)
Nonunitized zzz (EMU) magnitude was 7
Nonunitized zz (ONE) magnitude was 2.64575
squared: 7
ONE4: [P15 0.638161, 0.394405, 2.87637e-12, 2.22045e-16, 0.394405, 0.638161, 0.394405, 2.87637e-12, 0, 0.394405, 0.638161, 0.394405, 2.87614e-12, 2.22045e-16, 0.394405 ]
EMU5: [P15 3.46964e-12, 3.24255e-22, 0.52915, 3.46964e-12, 3.52379e-22, 0.52915, 3.46964e-12, 0, 0.52915, 3.46964e-12, 1.10465e-19, 0.52915, 3.46964e-12, 1.69407e-21, 0.52915 ]
Error: 2.19589e-11
Verified: EMU5^3 == ONE5 == ONE5*ONE5 (unitized)
Nonunitized zzz (EMU) magnitude was 7
Nonunitized zz (ONE) magnitude was 2.64575
squared: 7
ONE5: [P15 0.52915, 1.04089e-11, 2.40741e-35, 0.52915, 1.04089e-11, 0, 0.52915, 1.04089e-11, 2.40741e-35, 0.52915, 1.04089e-11, 2.40741e-35, 0.52915, 1.04089e-11, 0 ]
EMU6: [P15 0.168675, 0.581105, 0.0596637, 0.667327, 2.6567e-11, 0.697825, 0, 0.667327, 0.0596637, 0.581105, 0.168675, 0.454069, 0.308184, 0.308184, 0.454069 ]
Error: 3.61767e-11
Verified: EMU6^3 == ONE6 == ONE6*ONE6 (unitized)
Nonunitized zzz (EMU) magnitude was 7
Nonunitized zz (ONE) magnitude was 2.64575
squared: 7
ONE6: [P15 0.697825, 0, 0.667327, 0.0596637, 0.581105, 0.168675, 0.454069, 0.308184, 0.308184, 0.454069, 0.168675, 0.581105, 0.0596637, 0.667327, 4.51417e-13 ]
EMU7: [P15 0.168675, 0.454069, 0.667327, 0.667327, 0.454069, 0.168675, 6.57904e-12, 0.0596637, 0.308184, 0.581105, 0.697825, 0.581105, 0.308184, 0.0596637, 0 ]
Error: 6.09295e-11
Verified: EMU7^3 == ONE7 == ONE7*ONE7 (unitized)
Nonunitized zzz (EMU) magnitude was 7
Nonunitized zz (ONE) magnitude was 2.64575
squared: 7
ONE7: [P15 0.697825, 0.581105, 0.308184, 0.0596637, 3.25517e-13, 0.168675, 0.454069, 0.667327, 0.667327, 0.454069, 0.168675, 0, 0.0596637, 0.308184, 0.581105 ]

Sum of ONEs (EMUs^3): [P15 2.64575, 1.33826e-11, 1.24345e-12, 6.27942e-13, 8.81384e-12, 0, 8.83915e-12, 1.23452e-11, 2.20268e-12, 5.71143e-12, 1.45493e-11, 5.73586e-12, 1.39218e-11, 1.33045e-11, 1.16662e-12 ]

[Archimedes Plutonium]

Timba gone astray.

Forgetting that math comes directly out of physics, and values come from experimental measure, values among many values from Laws of physics.

But Timba wants to use Philosophy prattle when talking of mathematics, Timba too ignorant to use Physics when talking of mathematics.

[Timothy Golden]

Well the math has gone general dimensional so it does seem astray. Way back at the beginning spacetime support with unidirectional support was already found without any of this tripe. As to who betrayed dimension when they claimed the rational value fundamental: it seems everyone.

[zelos...@gmail.com]

>Ahhh... This bit 'on the set' is quite relevant.

Let's see you get things wrong and address nothing.

>Now, choose the set of real numbers and use an operator known as division.

Which is defined as multiplication by the inverse element and is not defined for 0

>This operator by your own system is defined on the preexisting set.

All operators are defined on sets.

>So are the rational numbers, which use division in their construction, in the set?

False, we construct the set of rational numbers as the set of ordered pairs in form of ZxZ_{>0}

Which I addressed already.

>It seems that by definition the division operator is already 'in the set' and so cannot be seen as 'on the set'.

This is just your ignorance, as I stated already in the previous post. We construct the set nad equivalence classes first, then operators.

>Then too, the choice of zero as in a/0 guarantees that the result is not in the set.

As stated, read up on constructions and you will see, that element does not exist and hence is invalid.

>Likewise the sqare root (sqrt(x)) suffers a similar trouble on negative numbers.

You didn't provide a trouble, all you provided was evidence that you do not know how rational numbers are constructed and we see the same issue here.

Sqrt is ordinarily not defined for negative real numbers, only positive numbers. When we have constructed complex numbers, for example R[X/<x^2+1>, can we extend the definition of sqrt such that it works on negative and complex numbers.

>You see, when you construct your set with an operator then your claim here about the operator being defined on the set is not valid.

again you are only demonstrating your ignorance. We make the set first, the operators after on the set. Learn how mathematics works for once in your fucking life.

[Timothy Golden]

Now to quote your own words above: "We make the set first, the operators after on the set."
And the rational numbers are an instance where this is not the case. This is exactly as I have discussed the concept from the outset, so on this quote we are in agreement and if it were true then the conflict should not be present. However all that I need to do is utter a rational value and we can see that the operator is in the set before the operators can be defined on the set, to reuse your own language which I do at least now see you are going to stick with. It amazes me how you can land your emotional criticisms right where we agree. To me the usage of rhetoric is in the reinforcement of a position rather than the abortion of one.

It's pretty clear to me that you see the problem. In essence you are confessing the correctness of my claim by dodging it. If the rational numbers were merely a set of ordered pairs ZxZ (and this is the first time you've used this language whereas you speak as if this has already come up) then I'd have more trouble to process. Fortunately I am looking back at the rationals from the reals; where the rationals fit on a line. Obviously division is in use, and the computability of a value such as 3/5 exposes this. There is an equivalent value up to any delta you care to specify. By your language we'd have no problem introducing more real numbers on ZxZxZ perhaps? No dimensional conflict whatsoever, right? Next thing you know you'll be deriving the real values as a subset of the real values and believing that you have achieved fundamental work.
Does 3/5 contain a division operation? Can I compute it? Is there an operator present? It seems that you are going to tell me 'no' and this will prove my position. The direct falsification of your own position is imminent. Here from Python the results are telling as well:
>>> print 3/5
0
>>> print 3.0/5.0
0.6
It's a shame that to even get to this ground with you will take so long. Still, for your persistence I have to give you credit, Z.

[Timothy Golden]

"We make the set first, the operators after on the set."

How strange it is then at the stage of developing the continuum that this rule was broken.

[FromTheRafters]

Timothy Golden explained :

> "We make the set first, the operators after on the set."
> How strange it is then at the stage of developing the continuum that this
> rule was broken.

How was it broken? To me it was the lack of set closure of inverse
operators which made extension and embedding necessary.

[Ross A. Finlayson]

I thought he meant linear operators with respect to operator algebras.

About the most usual arithmetic or what are the linear operators
with respect to usual fundamental arithmetic, there's something to
be said about the infinitely large and infinitely small and what
result "geometric mutations" as it were where the closures either
as they would complete or "skein free", operators are as much
the theorems and values the terms or vice versa.

[FromTheRafters]

Ross A. Finlayson pretended :

> On Monday, November 8, 2021 at 6:14:06 AM UTC-8, FromTheRafters wrote:
>> Timothy Golden explained :
>>> "We make the set first, the operators after on the set."
>>> How strange it is then at the stage of developing the continuum that this
>>> rule was broken.
>> How was it broken? To me it was the lack of set closure of inverse
>> operators which made extension and embedding necessary.
>
> I thought he meant linear operators with respect to operator algebras.

I think he means anything that sheds light upon his notion that a/b in
Q should be interpreted and stated as two elements and an operator
rather than as a single symbol for an ordered pair <a,b> element in Q
where both a and b are also ordered pairs of N in Z.

He seems to not like abstraction, but without it things get quite messy
very quickly.

[zelos...@gmail.com]

>Now to quote your own words above: "We make the set first, the operators after on the set."

and I bet misunderstanding yet again.

>And the rational numbers are an instance where this is not the case.

False, as I explained before you lying sack of shit

>his is exactly as I have discussed the concept from the outset, so on this quote we are in agreement and if it were true then the conflict should not be present.

There isn't a conflict. Only you being ignorant and willfully ignoring what I tell you.

>However all that I need to do is utter a rational value and we can see that the operator is in the set before the operators can be defined on the set

False, as I said and showed, we define the set for rational numbers, ZxZ_{>0}, then define equivalence classes, then define multiplication and addition, and from there we define the inverse operator and division operator.

>It's pretty clear to me that you see the problem.

There is no problem except your ignorance.

> In essence you are confessing the correctness of my claim by dodging it.

informing you where you are wrong is not confessing anything.

>If the rational numbers were merely a set of ordered pairs ZxZ (and this is the first time you've used this language whereas you speak as if this has already come up)

ZxZ_{>0}, this distinction is important.

>Fortunately I am looking back at the rationals from the reals

Which you cant because the reals are constructed after the rational numbers.

>Obviously division is in use

it is defined AFTER the set.

>and the computability

We aren't dealing with computers so irrelevant.

>By your language we'd have no problem introducing more real numbers on ZxZxZ perhaps?

If you can construct something meaningful on it go for it, it is doubtful it will be a subfield of R.

>No dimensional conflict whatsoever, right?

We aren't dealing with vector fields or modules so "dimension" is irrelevant.

>Next thing you know you'll be deriving the real values as a subset of the real values and believing that you have achieved fundamental work.

Of course not, that is circular you imbecile. You construct real numbers normally from Rational Numbers, either through dedekinds cuts or through cauchy sequences. Personally I love Eudoxus construction from integers.

>Does 3/5 contain a division operation?

It is a rational number.

>Can I compute it?
We are not dealing with computers!

>It seems that you are going to tell me 'no' and this will prove my position.

This proves my claim, that you are a complete fucking idiot.

>The direct falsification of your own position is imminent.

Nope, because again we are doing mathematics and you do not understand things.

>Here from Python the results are telling as well:

Irrelevant because we are dealing with mathematics, not computers.

>It's a shame that to even get to this ground with you will take so long. Still, for your persistence I have to give you credit, Z.

I do love showing how you idiots are all wrong and you are no exception. You are so very wrong :)

[Timothy Golden]

Spoken as if you cannot compute three fifths. As if the operator is not there.
Without the operator (division) the meaning of the rational values is naught.
Fit them to the line, sir. I am dealing in the real numbers. The real numbers contain the rational numbers.
How? Obviously this insistence on pairs of integers is not the case. The value 'a' is more often in use isn't it?
c = a / b
is exactly the issue at hand. On the right we see two values and an operator. On the left we see a singular value.
Under you lens c does not exist does it?

[zelos...@gmail.com]

There is nothign to compute, 3/5 is the rational number.

>As if the operator is not there.

There is no operator in an element, that is definitionally so.

7 does not have "an operator in it" just because we can write it 6+1

>Without the operator (division) the meaning of the rational values is naught.

False, because we could just as well write it (3,5) and it would be truer to the construction itself. We just do not out of historical habit.

>Fit them to the line, sir. I am dealing in the real numbers.

You don't, you talk about rational numbers. If you wanna discuss real numbers it is a slightly different story, then you gotta pick the construction itself.

>The real numbers contain the rational numbers.

To be more accurate, it contains a subfield that is isomorphic to the rational numbers.

>How? Obviously this insistence on pairs of integers is not the case. The value 'a' is more often in use isn't it?
>c = a / b
>is exactly the issue at hand.

That is not an issue.

>On the right we see two values and an operator.

You have 1 element on both sides.

>On the left we see a singular value.

there is only one element in both instances.

>Under you lens c does not exist does it?

it is an element like any other. The issue is that you focus on REPRESENTATION not what THEY ACTUALLY ARE

[Timothy Golden]

On Tuesday, November 9, 2021 at 12:57:14 AM UTC-5, zelos...@gmail.com wrote:
> >Now to quote your own words above: "We make the set first, the operators after on the set."
> and I bet misunderstanding yet again.
> >And the rational numbers are an instance where this is not the case.
> False, as I explained before you lying sack of shit
> >his is exactly as I have discussed the concept from the outset, so on this quote we are in agreement and if it were true then the conflict should not be present.
> There isn't a conflict. Only you being ignorant and willfully ignoring what I tell you.
> >However all that I need to do is utter a rational value and we can see that the operator is in the set before the operators can be defined on the set
> False, as I said and showed, we define the set for rational numbers, ZxZ_{>0}, then define equivalence classes, then define multiplication and addition, and from there we define the inverse operator and division operator.

Really? It seems to me that you have gotten yourself into a pickle here. Lets consider addition of the set ZxZ, and we'll neglect sign if you like. Arguably I must since it is my duty to insert sign back in at a later stage. We are concerning ourselves, I believe on a first version of a continuum. Yet as we look at the addition operation on ZxZ, pretty clearly we are not getting what you think we are going to get. You are going to have to create some sort of anti-number and twist an operator out your opposing end. Well, lo and behold we can witness the form 1/Z and yield the first inklings... and yet these values will all merely be a repositioned one. All will take the constant 0.1. All is well for my side here. You are a dirty reradixer.

> >It's pretty clear to me that you see the problem.
> There is no problem except your ignorance.
> > In essence you are confessing the correctness of my claim by dodging it.
> informing you where you are wrong is not confessing anything.
> >If the rational numbers were merely a set of ordered pairs ZxZ (and this is the first time you've used this language whereas you speak as if this has already come up)
> ZxZ_{>0}, this distinction is important.
> >Fortunately I am looking back at the rationals from the reals
> Which you cant because the reals are constructed after the rational numbers.
>
> >Obviously division is in use
>
> it is defined AFTER the set.

I'm awaiting addition in a sensible manner on your new found fabrication. Did you want to implement an operator swap or an operator swamp?
I do still understand the language of draining the swamp. Yet at the same time it is just an analogy. Swamps as natural places can be good things. We have quite a lot of them where I live. There are pitcher plants though they can be difficult to spot. Cranberries too. Not sure how they are doing this year yet.

>
> >and the computability
>
> We aren't dealing with computers so irrelevant.

The fact that you would deny this is an indicator. Humans were the first computers. Machines took the human's name. And yes, mathematicians are still computers, and when they throw this identity away, as I've already stated, an indication of what is to come creeps in.

> >By your language we'd have no problem introducing more real numbers on ZxZxZ perhaps?
> If you can construct something meaningful on it go for it, it is doubtful it will be a subfield of R.
> >No dimensional conflict whatsoever, right?
> We aren't dealing with vector fields or modules so "dimension" is irrelevant.

Certainly we are. The real number is one dimensional by definition. Fascinating to see once again the standard mathematical error of being off by one.

> >Next thing you know you'll be deriving the real values as a subset of the real values and believing that you have achieved fundamental work.
> Of course not, that is circular you imbecile. You construct real numbers normally from Rational Numbers, either through dedekinds cuts or through cauchy sequences. Personally I love Eudoxus construction from integers.
> >Does 3/5 contain a division operation?
> It is a rational number.

I think this was more a yes/no type of question.
I think again we have a strong indicator here.
Aren't there times when they come clean?
Did you really want to confuse the issue on
10/2 = 5 ?
Is it really an different on
9/2 = 4.5
Hmmm... two values on the left and an operator... one value on the right and no operators.... hmmmm....
Did I do something wrong?

>
> >Can I compute it?
> We are not dealing with computers!
> >It seems that you are going to tell me 'no' and this will prove my position.
> This proves my claim, that you are a complete fucking idiot.
> >The direct falsification of your own position is imminent.
> Nope, because again we are doing mathematics and you do not understand things.
> >Here from Python the results are telling as well:
> Irrelevant because we are dealing with mathematics, not computers.

This must be considered a bittersweet divorce that you've engaged in here.
The computers are so much faster than the humans now.
It's almost like I'm speaking to Pythagoras.
I suppose you can take that as a complement, but I don't mean it that way.
Ahh, but it is appropriate isn't it?
The mature form of the conversation here will evolve into numeric types.
We know that the integers as a set cannot bear nonintegers through operators and still abide by closure.
I suppose taking the rational number a level simpler we could therefor conclude that the integers are not closed.
And yet doing division integer style did yield a double value. You get a whole part and a remainder.
I remember answering like "3r6" when I was a kid.
This line of reasoning though is exactly what you dodge in your zxz implementation. This is the cause of your sidetrack.
How could it be that the product is closed yet the inverse of the product is not closed?
The answer lays in the fact that division is a reverse operator. In hindsight if
c = a * b (* being the arithmetic product)

then

c / a = b

and this is the true meaning of division in its pristine state. And yet we will be forced still to introduce an exception.
Well, the quantity of exceptions rises in higher dimension and the support for my claim grows up there.
Division is not such a paltry thing as some would like it to be.
Your own language of 'subfield' somewhere in your post here is suspect.
But this can be seen as an aside I think rather than at the front of this discussion.

> >It's a shame that to even get to this ground with you will take so long. Still, for your persistence I have to give you credit, Z.
> I do love showing how you idiots are all wrong and you are no exception. You are so very wrong :)

Well my words are here to be falsified aren't they? Instead you seem to be relying upon rhetoric without falsification. Already I've got a small pile going on the status quo system. Then too on the philosophical side I should harken back to the dubious nature of deriving a continuous system from a discrete system. It's sort of chicken and egg, and they you throw in zxz as if you've swamped things. Yes, you have. I've seen this sort of reasoning before as well. On the point of confusion throw in something even more confusing and wipe away the first point of contention. It's like the windshield cleaning guys in the city hiring a kid to throw soda on your windshield first. That sort of behavior is not supposed to go on in mathematics is it?

[Mostowski Collapse]

Congratulations timba, you have the only geometric
user icon here in google groups. Not like AP brain fartos
user icon, that looks like a pile of shit.

No wonder, AP brain farto only produces shit after shit
every day. Not a single line of math.

[Mostowski Collapse]

Lets make November 2021 the month of nice math icons.
Slap them into the face of the brown cockroaches, such as
AP brain farto that have shit icons. Just like the shit

they produce every day. Not a single line of math.

[Timothy Golden]

On Monday, November 8, 2021 at 2:05:06 PM UTC-5, FromTheRafters wrote:

No, Rafters. I repeat again that I am in the real numbers. You are so stuck in these pairs that you will not be able to admit that
6/2 = 3
will you?

My argument ultimately is that when the reals absorbed the rationals that something invalid happened. The construction of a number system should not carry operators internally like this. Again my logic is simply an awareness of two distinct concepts of operators and values. To mix these two up and call the system fundamental is a lie. In hindsight our decimal values suffice as integers and the decimal point as a mark of unity along with epsilon/delta applying to every value makes a better interpretation. The continuum becomes gray under this thinking. You can chase digits, but generally close enough is good enough. This then is the nature of the continuum which has been struggled over. At bedrock there is an argument on materiality here as well. Without material the mathematician would have little to go on. For instance the practical nature of counting how many pencils are left in the box. Of course the material situation goes on from there, and the number of pencils sitting on your keyboard might be relevant too. I doubt very much though if the quantity of pencils in your town is of interest, unless of course you are witnessing a pencil shortage. The point is much more serious as we engage in a complete divorce of mathematics from the material world. I do argue that this divorce is invalid. The physicist will understand. The engineer will understand, and yet the poor mathematician will sit in his cell pondering an eternity of immateriality. Yet we claim to use his real number. I suppose that deep down this topic may require the wielding of this materiality argument. The mathematician cannot mark down 3/5 on a line better than a physicist. Where issues of a continuous nature truly play a part the usage of the rational value has done nothing for humanity. I would think that there are some clever falsifications of this claim, but none are coming to mind at the moment.

Really I think it is apparent to a bystander that the crisis here is on your side: you own inability to admit that the rational value is composed of two values and a division operator. That you are cornered by this simple statement is a damning aspect of each of your positions. For now it seems you willingly adopt the pair of values, and claim them to be one value? Hmmmm. what sort of construction does such things? The distinction of values and operators is such a primitive notion that has been broken by mathematics and really this narrow instance is just one position.

For myself I am forced to address the rudimentary form and of
s x
where s is sign and x is magnitude, and is this a product? Then too, as we do products and sums on these rudimentary values why is addition of signs in the product? This awareness goes on and on and into abstract algebra where I've posted several threads here disputing the polynomial and closure. The one thing that is very clear in the instance above is that sign is of a different type than magnitude. This feature alone is nearly impossible for the mathematician to grasp; otherwise polysign numbers would have been invented ten times over by men far brighter than I. It honestly does stupefy me how they have gone overlooked for this long. As I stumble along in the fundamentals I see now that sign has only barely really been adopted. Perhaps the decimal point too. Many maintain their pursuit of the natural value as fundamental, with nothing left to ponder other than infinity. Meanwhile every value is being carried by the physicist ultimately as a natural value stitched with a few more qualities. The representation that we have is fine, but its interpretation is abysmal.

[FromTheRafters]

Timothy Golden formulated on Tuesday :

> On Monday, November 8, 2021 at 2:05:06 PM UTC-5, FromTheRafters wrote:
>> Ross A. Finlayson pretended :
>>> On Monday, November 8, 2021 at 6:14:06 AM UTC-8, FromTheRafters wrote:
>>>> Timothy Golden explained :
>>>>> "We make the set first, the operators after on the set."
>>>>> How strange it is then at the stage of developing the continuum that this
>>>>> rule was broken.
>>>> How was it broken? To me it was the lack of set closure of inverse
>>>> operators which made extension and embedding necessary.
>>>
>>> I thought he meant linear operators with respect to operator algebras.
>> I think he means anything that sheds light upon his notion that a/b in
>> Q should be interpreted and stated as two elements and an operator
>> rather than as a single symbol for an ordered pair <a,b> element in Q
>> where both a and b are also ordered pairs of N in Z.
>>
>> He seems to not like abstraction, but without it things get quite messy
>> very quickly.
>
> Spoken as if you cannot compute three fifths. As if the operator is not
> there. Without the operator (division) the meaning of the rational values is
> naught. Fit them to the line, sir. I am dealing in the real numbers. The real
> numbers contain the rational numbers. How?

They are embedded. Think bottom-up rather than top-down. Embedding
carries the agebraic structure of the lower previously defined number
system to the newer one. The naturals are not really a subset of the
integers, the naturals are embedded in the integers.

> Obviously this insistence on pairs of integers is not the case.

It is the issue if you insist upon not hiding what items are actually
made of. One might like to know when working in the reals that a
particular "fraction" is constructed from integers a and b rather than
from reals. If a and b are integers, the result is in Q. Integers are
ordered pairs of naturals, and the naturals are embedded in Z as
ordered pairs.

The value 'a' is more often in use isn't it? c =
> a / b is exactly the issue at hand. On the right we see two values and an
> operator. On the left we see a singular value. Under you lens c does not
> exist does it?

Then c is simply the element of of Q which represents the symbol a/b
(ordered pair <a,b>) which is simply the result of the inverse
operation to multiplication.

[FromTheRafters]

Timothy Golden formulated on Tuesday :

> On Monday, November 8, 2021 at 2:05:06 PM UTC-5, FromTheRafters wrote:
>> Ross A. Finlayson pretended :
>>> On Monday, November 8, 2021 at 6:14:06 AM UTC-8, FromTheRafters wrote:
>>>> Timothy Golden explained :
>>>>> "We make the set first, the operators after on the set."
>>>>> How strange it is then at the stage of developing the continuum that this
>>>>> rule was broken.
>>>> How was it broken? To me it was the lack of set closure of inverse
>>>> operators which made extension and embedding necessary.
>>>
>>> I thought he meant linear operators with respect to operator algebras.
>> I think he means anything that sheds light upon his notion that a/b in
>> Q should be interpreted and stated as two elements and an operator
>> rather than as a single symbol for an ordered pair <a,b> element in Q
>> where both a and b are also ordered pairs of N in Z.
>>
>> He seems to not like abstraction, but without it things get quite messy
>> very quickly.
> No, Rafters. I repeat again that I am in the real numbers. You are so stuck
> in these pairs that you will not be able to admit that 6/2 = 3
> will you?

Sure, two different representations of the same number are equal. Even
in the reals these numbers are in the same equivalence class.

> My argument ultimately is that when the reals absorbed the rationals that
> something invalid happened. The construction of a number system should not
> carry operators internally like this. Again my logic is simply an awareness
> of two distinct concepts of operators and values. To mix these two up and
> call the system fundamental is a lie.

My contribution was to attempt to show you that the same thing happened
from sets to natural numbers (we simply re-labeled them) and from
natural to integers and from integers to rationals. Without abstraction
we would be doing squareroots of multiply nested and adjoined sets of
sets containing the emptyset.

As a side note, we speak of arrangements as states and permutations as
actions where Galois had them reversed. This shows, from an earlier
conversation, how nouns can become verbs and vice versa.

[Gregor Bicha]

Mostowski Collapse wrote:

> Lets make November 2021 the month of nice math icons.
> Slap them into the face of the brown cockroaches, such as AP brain farto
> that have shit icons. Just like the shit
>
> they produce every day. Not a single line of math.

okay

[Timothy Golden]

I am amazed at how readily you dodge the operator.

[Timothy Golden]

On Tuesday, November 9, 2021 at 8:21:33 AM UTC-5, FromTheRafters wrote:

Ooohhh. Here you almost squeak it out:
'Yes, Tim, that is also known as a divided by b, and sure enough we can resolve such a value to a singular value with no operator in it whatsoever." Oh, gee, thanks Rafters...
The analysis remains. Honestly the status quo position is being exposed as weak by you.

[Archimedes Plutonium]

Tim, you are on to something good here in this thread. Good enough for me to respond. But I think your philosophy based approach is not going to give any payback. Instead if you have a Physics approach where All is physics and that mathematics is a mere subset.

So you start with math has numbers and algebra because atoms are numerous. And math has geometry because atoms have shape and size.

As for the question of dimension, always-- look to physics, not to the worthless imagination of a mathematician. In Physics we have no dimension beyond 3rd for the Maxwell Equations in Old Physic, mind you in Old Physics they could prove that no EM theory goes beyond 3rd dimension. In fact, most of electricity and magnetism is 2 dimensional. So if Physics cannot have 4th dimension, very silly for the silly and stupid mathematician waffling on about higher dimensions.

[Timothy Golden]

Thanks AP. I know it is rare for you to say such nice words. I do appreciate your support.
I'm pretty sure that even from the basis of mathematical analysis the rational can cave in.
There are areas of ground to cover that we can't even get to here because these guys can't even move to admit that the rational value inherently contains the division operation. Next on the agenda is to ask whether a value such as
1.23
is a rational value? Where are the two parts? I am developing a new position on this that claims this decimal value is an integer 123 with a little dot added to its structure. The structure is rather different than the rational value. Clearly unity is the third digit up, and this is the meaning of the decimal point. Other than that this is a reinterpretation of the standing integer. The mechanism of the decimal value is the same mechanism as the integer. These are radix ten concepts. The value is gray to the right of the last digit. This is exactly the physicists interpretation of that value. This is how the material world works. Yes, when we are good we can chase down some more digits, but they do require chasing. It is amazing how many digits some of physics can get actually. Then again on other features not so good. Still the math must go on. We do not stop because we do not have perfection.

[Archimedes Plutonium]

Yes, I think I can help out on this Operators versus Values. There is nothing wrong with operators. There is much wrong with how Old Math defines numbers.

In my textbook TEACHING TRUE MATHEMATICS: Volume 2 for ages 5 to 18, math textbook series, book 2
by Archimedes Plutonium 2019.

I teach that Rationals are not numbers at all, but are Unfinished Division problems. To say that 2/3 is a number is like saying 2/giraffes is a number of mathematics.

This is a very subtle mistake of Logic that Old Math made. For what they did was hold some sort of circus auction on a campus campground, and any one showing up with a bag ful of so called numbers were invited and their bagful was claimed as numbers of mathematics.

When the only numbers that exist are Decimal Grid Numbers all begot not from idiots offering Rational bag, Irrational bag, Complex bag, Real bag.

All numbers come from just math induction. So then, 0.6 is a true number in 10 grid, 0.66 a true number in 100 Grid, etc. but 2/3, well that is a clown who has a bag of unfinished division idiocy and wants to think his worthless bag of objects are numbers of mathematics. No, there is no number 0.666.... nor is there 0.999.... all unfinished and mindless objects in the Rational bag of nonsense.

The only numbers that exist come from Mathematical Induction and are members of a Decimal Grid System.

[Timothy Golden]

On Tuesday, November 9, 2021 at 5:25:20 PM UTC-5, Archimedes Plutonium wrote:
> Yes, I think I can help out on this Operators versus Values. There is nothing wrong with operators. There is much wrong with how Old Math defines numbers.
>
> In my textbook TEACHING TRUE MATHEMATICS: Volume 2 for ages 5 to 18, math textbook series, book 2
> by Archimedes Plutonium 2019.
>
> I teach that Rationals are not numbers at all, but are Unfinished Division problems. To say that 2/3 is a number is like saying 2/giraffes is a number of mathematics.
>
> This is a very subtle mistake of Logic that Old Math made. For what they did was hold some sort of circus auction on a campus campground, and any one showing up with a bag ful of so called numbers were invited and their bagful was claimed as numbers of mathematics.
>
> When the only numbers that exist are Decimal Grid Numbers all begot not from idiots offering Rational bag, Irrational bag, Complex bag, Real bag.
>
> All numbers come from just math induction. So then, 0.6 is a true number in 10 grid, 0.66 a true number in 100 Grid, etc. but 2/3, well that is a clown who has a bag of unfinished division idiocy and wants to think his worthless bag of objects are numbers of mathematics. No, there is no number 0.666.... nor is there 0.999.... all unfinished and mindless objects in the Rational bag of nonsense.
>
> The only numbers that exist come from Mathematical Induction and are members of a Decimal Grid System.

Well, the purity of the real value is supposed to be quite some stage of formalization, and yet when you see that epsilon/delta applies to some values and not to other values... the gig is up.

I agree, and there is a small circus show going on in the real value.

Universal; Unification; these concepts are antithetical to that sort of mathematics.

[zelos...@gmail.com]

>Really? It seems to me that you have gotten yourself into a pickle here.

Only because as always, you are ignorant as fuck.

>Lets consider addition of the set ZxZ, and we'll neglect sign if you like.

We cannot ignore it because the fact that the second does NOT contain 0 is important! So if you bring up 0 your argument is invalid.

>I believe on a first version of a continuum.

Not really, it is about constructing a field from Z

>Yet as we look at the addition operation on ZxZ, pretty clearly we are not getting what you think we are going to get.

We do, we get a field that works and behaves just like Q :) keep in mind addition [(a,b)]+[(c,d)] is defined as [(a,b)]+[(c,d)]=[(ad+bc,bd)]

>You are going to have to create some sort of anti-number and twist an operator out your opposing end.

This is non-sense

>Well, lo and behold we can witness the form 1/Z and yield the first inklings

What are you on about?

With the definition [(a,b)]*[(c,d)]=[(ac,bd)]

we define the inverse [(a,b)]^-1=[(b,a)]

and in turn [(a,b)]/[(c,d)]=[(a,b)]*[(c,d)]^-1=[(ad,bc)]

>... and yet these values will all merely be a repositioned one. All will take the constant 0.1. All is well for my side here. You are a dirty reradixer.

You are talking non-sense and no mathematics to adress here.

>I'm awaiting addition in a sensible manner on your new found fabrication.

New found? this is old and considered the standard method to construct rational numbers from integers.

>Did you want to implement an operator swap or an operator swamp?

on what? I have done nothing of the sort.

>The fact that you would deny this is an indicator.

yes, it is indicative of we are not DEALING WITH COMPUTERS! mathematics is not about computers! Computers cannot do mathematics!

>Humans were the first computers.

Humans are not computers. Biological brains and computers work on fundamentally differnet principles.

>Machines took the human's name. And yes, mathematicians are still computers, and when they throw this identity away, as I've already stated, an indication of what is to come creeps in.

They aren't. The analogy is often used because simpletons like you have a hard time understanding how the brain works. A brain and a computer works in fundamentally different things, that is why brains are good at some things, computers are good at others.

>Certainly we are.

Nope, we are not.

>The real number is one dimensional by definition.

Nope, it is only that when you look at it as a vector field over the Real Numbers.

But when you look at the real numbers as a field, it is meaningless to discuss dimension.

>Fascinating to see once again the standard mathematical error of being off by one

Nope, the error is your knowledge being limited you ignoramus.

>I think this was more a yes/no type of question.

Think what you want, I won't play your games and I will answer questions as the truth stands.

>I think again we have a strong indicator here.
>Aren't there times when they come clean?

Are there times hwen you will admit you are an idiot?

>Did you really want to confuse the issue on
>10/2 = 5 ?
>Is it really an different on
>9/2 = 4.5

Two elements in the same equivalence class. Big deal.a

>Hmmm... two values on the left and an operator... one value on the right and no operators.... hmmmm....

False, one element on the left, one element on the right. Both in the same equivalence class.

>Did I do something wrong?

yes, you didn't get a fucking education and got stuck at what is NOTATION instead of understanding WHAT THINGS ARE.

>This must be considered a bittersweet divorce that you've engaged in here.

Nope

>The computers are so much faster than the humans now.

In arithmetic, humans are not good at that. We are much better at proving things :) Computers have yet to do that. No computer has been able to pump out the proof that the continuum hypothesis is independent of ZFC.

>We know that the integers as a set cannot bear nonintegers through operators and still abide by closure.

You don't need to say it like that. The integers contain only themselves BY FUCKING DEFINITION.

>I suppose taking the rational number a level simpler we could therefor conclude that the integers are not closed.

We can conclude nothing of the sort because the ring (Z,+,*) has no division and only contains + and * and both are closed.

>And yet doing division integer style did yield a double value. You get a whole part and a remainder.

Once again you are not understanding things.

>I remember answering like "3r6" when I was a kid.

that is where you still are intellectually. A kid. You have not grown since then and only think in those pathetic stupid ignorant terms rather than learn how ACTUAL mathematics go about defining things!

>This line of reasoning though is exactly what you dodge in your zxz implementation. This is the cause of your sidetrack.

No, it is caleld using ACTUAL DEFINITIONS and not HIGHSCHOOL SHIT.

>How could it be that the product is closed yet the inverse of the product is not closed?

it is closed, integers only got + and * that are closed.

>The answer lays in the fact that division is a reverse operator. In hindsight if
>c = a * b (* being the arithmetic product)
>then
>c / a = b

incorrect, division is defined as multiplication by inverse and the inverse is defined such that a^-1*a=a*a^-1=1

>and this is the true meaning of division in its pristine state. And yet we will be forced still to introduce an exception.

That is HIGHSCHOOL understanding! Why won't you learn ACTUAL mathematics!?

>Your own language of 'subfield' somewhere in your post here is suspect.

Why, because you are too stupid to understand what it fucking means?>

>Well my words are here to be falsified aren't they?

I have shown you wrong at every point.

>Instead you seem to be relying upon rhetoric without falsification.

False, I have shown you wrong with definitions and what things are. All you do is go on about highschool shite.

>Already I've got a small pile going on the status quo system.

No, you got NOTHING but ignorance.

>Then too on the philosophical side I should harken back to the dubious nature of deriving a continuous system from a discrete system.

We have logically constructed rationals and real numbers from previous structures. That is how number construction works.

>It's sort of chicken and egg

Nope, it is a clear path. N then Z then Q then R then C then H etc

>and they you throw in zxz as if you've swamped things.

I throw nothing, I just tell you how the construction is done in mathematics. It is not my fault you're fucking ignorant.

>On the point of confusion throw in something even more confusing and wipe away the first point of contention.

it is not confusing, it is you being an idiot. If you do not understand these basic mathematical structures and constructions, STAY THE FUCK AWAY!

[zelos...@gmail.com]

nothing is going on but you being ignorant

[zelos...@gmail.com]

How are you going to add anything when you are too stupid to get basic mathematics, physics AND biology!?

[zelos...@gmail.com]

>Thanks AP. I know it is rare for you to say such nice words. I do appreciate your support.

When a huge crank speak that nicely, it means you are so fucking wrong you should turn around and run away.

>I'm pretty sure that even from the basis of mathematical analysis the rational can cave in.

Nope, it follows logically. The issue is that you have no understanding beyond pre-high school

>There are areas of ground to cover that we can't even get to here because these guys can't even move to admit that the rational value inherently contains the division operation.

It doesn't. [(3,5)] has no "division" in it, it is just an ordered pair, that is what a rational number is in construction.

>Next on the agenda is to ask whether a value such as
>1.23
>is a rational value?

1.23=123/100=[(123,100)]

so yes, stop asking stupid questions.

>I am developing a new position on this that claims this decimal value is an integer 123 with a little dot added to its structure.

There is no structure there, there is just NOTATION. You ALWAYS fail to understand the difference between notation and the object.

>The structure is rather different than the rational value.

Nope, that too is an ordered pair or equivalent to one through a monomorphism.

This demonstrates your ignorance perfectly as always.

You do not understand ordered pairs
You do not understand number construction
You do not understand notation
You understand quite literally NOTHING of the fundamental mathematics that you want to attack!

[Timothy Golden]

On Wednesday, November 10, 2021 at 3:12:49 AM UTC-5, zelos...@gmail.com wrote:
> >Thanks AP. I know it is rare for you to say such nice words. I do appreciate your support.
> When a huge crank speak that nicely, it means you are so fucking wrong you should turn around and run away.
> >I'm pretty sure that even from the basis of mathematical analysis the rational can cave in.
> Nope, it follows logically. The issue is that you have no understanding beyond pre-high school
> >There are areas of ground to cover that we can't even get to here because these guys can't even move to admit that the rational value inherently contains the division operation.
> It doesn't. [(3,5)] has no "division" in it, it is just an ordered pair, that is what a rational number is in construction.
> >Next on the agenda is to ask whether a value such as
> >1.23
> >is a rational value?
> 1.23=123/100=[(123,100)]

This I do think matters. I did scan your other posts and I see you are serious about staying on here.
As to what is fundamental: isn't it true that what is simpler is more fundamental?
That 1.23 does not seem to describe any operator. It is purely value.
Yes, there is additional notation, yet the form remains within the radix ten rules which already get us our large values.
Of course scientific notation is not far away. But we don't actually need the two-signed exponent of ten.
We are literally reassigning where unity lays on the value. This value has only just crept beyond the original.
Certainly we see that it is a far more restrained form than the general rational value. This is how I can target the traditional thought pattern as that of the dirty reradixer.
If you would like to do your work in ninths that will be fine, but the assumption is that we work in ten by convention. And then of course comes the ambiguity that every radix counting system is radix 10. Thusly to disambiguate here my language ought to go either:
"If you would like to do your work in 111111111 that will be fine..."
or
"...the assumption is that we work in 1234567890 by convention."
and at this position in the conversation of fundamental things where assumptions must be stated clearly because the work is so low as to deserve this level of treatment, we witness our dependence upon modulo behaviors. These same behaviors do in fact arise through division. However the earlier form of these behaviors is in systematic counting, and because the systematic counting is going to be used within your division analysis it clearly comes first. Thus it is the more fundamental of the two.

Here again I cannot claim to be fully in the clear, for these counting mechanisms in their own way carry ongoing zero exceptions. There is a little rod on the wheel of digits 1234567890 (these forming a ring already) which connects to teeth on the next digit up. Iconically in your head possibly you are seeing these digits dancing; the lower digits whirring away rapidly down to some level where they go gray and beyond what you perceive as gray even more grayly gray. There lays the unknown. Without this mechanism we cannot discuss the value 101. We are back at the early stages of mathematics. To destroy the modulo/radix system is to go without any large values. At the very least we can call math which does so uninstantiable. It happens that there is quite a lot of uninstantiable mathematics, so you wouldn't be alone in going there... it's just that you left yourself in a cell of immateriality in the process. Oh, gee, wait. There is the primitive mathematician who states:
Let n = 11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111.
Well, it is fitting on one line in my editor here. This is by the way the modulo one form. It is arguably a serious type; just not the type that we generally do our work in. No, we have agreed in a compact to abide by the ten digits. Come now, can't you see that the decimal point is merely a tacked on structure? It is however of a different type isn't it? Whereas the rational value requires two of the original value and an operator the decimal point is a different type. Obviously in our standard notation it is a little dot. And nicely enough we do not see any operator yet if we were to grant an operator to the decimal point it would be as a product relation; a fundamental operator.

So I believe that I have substantiated a strong difference and preference for 1.23 as more fundamental than 123/100. And here we have returned around in circular fashion to our old discussion point where you claim that two values and an operator are one value, and I continue to hold my ground, though now my ground is a bit better footed on the argument I have just provided.

Zelos, I do appreciate your ongoing participation here. You did manage to provide addition as a more complicated operation than division which is quite an improvement, eh? Keep up the good work.

[Ross A. Finlayson]

It seems like the usual abstraction of rationals is "real-values of reduced fractions",
w.r.t. an algebra's field and the usual. Then, it seems that for augmenting the system
where 3/2 and 6/4 are distinct, is about some matters of scale, that instead of the
usual origin and the line that instead it's destination and bounds.

Not sure I much get it....

The polysign values themselves seem more clear-cut, so Timothy I'm not quite
sure what you're railing about, though it seems as about a usual distinction
between "out from zero" and "into zero", or with respect to usual ratios of 1/oo
or here as about some oo/oo.

[Timothy Golden]

Thanks Ross for what looks like an honest assessment. I should be careful not to interject polysign into this discussion. The criticism of the rational value is free standing. Though I did arrive at it through polysign, it has been the long way around with operator theory really the crux of the argument here. It was sort of baffling to bump into it, honestly.

Historically speaking the rational value is an elder, and I should treat it respectfully, yet is it fundamental? According to real analysis it is. According to my analysis here it is not. This is one simple rendition or debriefing without getting into the obscurities. That said we can only round the discussion out by getting into those obscurities.

To what degree are the rational sixths merely radix six values? The radix system suffices without the rational analysis, which many here are having a hard time facing.

Z has done a good job exposing himself. He has claimed that the values must be built before the operators can be applied to them. If the rational values build a number system then he is caught denying that the division operator exists. This is not only Z's problem. Even Rafters here can barely let it squeak out. Z has started to substantiate operators on rationals that make addition look more complicated than division. I assure you that it is the other way around. He is going to have exceptions in his addition I suspect. The rational value as fundamental fades under this scrutiny.

Meanwhile we had integers without division. Yes, the formalities do call for a successor function, which looks obnoxiously like an increment operation (embedded addition operator), but this sort of offense is very mild in comparison to the rational value. My argument is somewhat supported by the successor function as it hides the operator. Any way there are all sorts of side shutes like this to consider as this analysis is intended to apply generally. It is roughly the same criticism that I have put to the polynomial of abstract algebra in the past. I do not mean to go to that topic, as it has been covered already.

To ground out in simplicity simply ask yourself: are operators and values distinct concepts?
If you cannot answer yes to this question then the struggle that you face is suspicious.
Well, you have learned under threat of failure, and so you have been conditioned.
Good luck with that.

[Timothy Golden]

On Sunday, November 7, 2021 at 3:57:02 PM UTC-5, Timothy Golden wrote:
> On Sunday, November 7, 2021 at 1:03:00 PM UTC-5, Serg io wrote:
> > On 11/7/2021 7:19 AM, Timothy Golden wrote:
> > > On Saturday, November 6, 2021 at 10:37:57 AM UTC-4, Timothy Golden wrote:
> > >> On Friday, November 5, 2021 at 5:40:33 PM UTC-4, Serg io wrote:
> > >>> On 11/5/2021 3:59 PM, Timothy Golden wrote:
> > >>>> On Friday, November 5, 2021 at 1:03:20 PM UTC-4, Serg io wrote:

> > >>>>> On 11/2/2021 9:17 AM, Timothy Golden wrote:
> > >>>>>> When operators came to be embedded into numbers then mathematics lost integrity.

> > >>>>> wrong.
> > >>>> I would think that it is fair to state that the real numbers are built atop division.
> > >>>> Division as an operation is in the set of real numbers isn't it?
> > >>>> This statement goes in distinction to your own :
> > >>>> 2. Division is a binary operation defined on the real numbers.
> > >>> division is a "binary input, unitary output" operation,
> > >>> a number compressor, two go in, one comes out. 60/10 = 6
> > >>>
> > >>> but addition is "many in, one out" operation 1+1+1+1+1 = 5
> > >>>
> > >>> factorization is "one in, many out" 60 = 2 * 5 * 2 * 3
> > >> Pretty sure as division is a reverse operation of the product that a multiple form could exist:
> > >> 60 / 2 / 5 / 2 / 3 = 1 = ((((60 / 2) / 5) / 2) / 3)
> > >> My compiler likes it.
> > >> But clearly division (and subtraction) are not commutative, whereas the product is.
> > >> The product is the more fundamental operation.
> > >> This is born out in abstract algebra.
> > >> The fact that a reverse operator is in use in the construction of a number system known as the real numbers is problematic.
> > >>
> > >> Much of this is a sidetrack though. The inability to strike the nail on the head with the hammer here is abysmal.
> > >> If the fundamentals are broken then what of the pile? More on this later. More on this in the past. More on this now.
> > >> It has to be considered that mathematics tries to play nice historically speaking. It tries to be more like a series of rungs on a ladder, but it does branch and rerung. How much of that structure lays on a faulty branching or footing is troubling if the flaw is found down low. The extraordinary inattention to operator theory as a serious pursuit is born and reborn and yet as it is passed beneath our noses nobody seems to smell a thing. It is not our option to falsify this subject. It is enforced that if you fail to mimic then you fail. I guess I am some sort of matheist. Ah, but I do not wish to throw the whole thing away. I can own that I am a social animal whose behaviors are suspect at a level beneath conscious reasoning.
> > >>
> > >> The grammatical analysis is actually quite striking in its appropriateness. If any should make it to a new grammatical structure its adoption by others will be challenging. If wee humans are lacking a grammatical option by genetic limitation it would explain quite a bit. That this could show in mathematics would be quite a plight. Still, if this were the truth it would be no time to shy away.
> > >>
> > >> The reverse operator known as division as well carries an exception. Sadly this is not the end of it. In higher dimension the quantity of exceptions rises. The field axioms are a false start. The product itself suffers none of this. Sure, information can be destroyed through the product, and so never to be recovered again (the reverse operation) but it were not true that
> > >> a * b = c
> > >> then it will not be true that
> > >> c / a = b , c / b = a .
> > >> These latter are more results than they are fundamental constructions. Likewise and nearby is the square root. When
> > >> x * x = y
> > >> then we know that x is a square root of y. The fancy modified division symbol somehow has come to be adopted as if the expression is a raw value. The treatment of variables and constants and actually concrete values is not actually careful enough in mathematics. Particularly when I can express an ambiguity with concrete values then we are down onto something very fundamental. That the abstraction away to 'a' as a value relaxes some of that tension is not actually helpful. A few more steps along and we see entire branches of mathematics composing properties of objects that are completely lacking instantiable forms. Then when an instance pops up it appears to be so trivial that the complexity of the language becomes suspicious. It is unclear to me how much of mathematics is beyond my ability to absorb or how much of it is not worthy of absorption. So I can only plod along and announce falsifications as I bump into them. This attack on the rational value is a bump that I was not looking for. Yet here it is.
> > >>
> > >> You have failed to own or correct your language of the operator as defined 'on' the set, as if the set pre-exists the operator. You have failed to register the fact that the rational value relies upon division to develop the set of real numbers, which is in contradiction to that first statement in this paragraph. That said, you are putting in a decent effort here, Z. Thank you for holding the establishment line. Best of all this is a very simple concept that we are discussing, so I do believe that the truth can be found. The radix mechanism lives nearby. We adopted it first and its reuse here is very sensible.
> > >>>
> > >>> so, where are you going with this ?
> > >>>>
> > >>>> Because the meaning of the distinction is so directly about nouns (values) and verbs (operators)
> > >>>> it does become appropriate doesn't it to talk about these types distinctly. How blunderous it feels when they then take same meaning.
> > >>>> Will you deny me my own grammar?
> > >>> not at all, I improve it.
> > >>>
> > >>>> Is yours so superior?
> > >>>
> > >>> Yes.
> > >>>
> > >>>> Or is it parallelism?
> > >>>
> > >>> Never.
> > >>>> No: I falsify your method here. Yet we upon the same grammatical form. I say your operator is in the set. I say my operator is on the set; outside of it; something which comes later and ought not be confused with the set itself. One is action: the operator. The other is value: the material. Ahhh, here we are bridging into philosophy possibly, this notion of material and by it I do mean the physical: without the material there is no count. Show me one who learns to count without material. Well, you go to material as waves rather quickly to get anything sensible, and so it has occurred. Rather than shall we just say that waves are material and that the prior holds? Yes, I'll take that.
> > >>>>
> > >>>> Now when we discuss the concept of a verb the strictness is quite direct and nonsensible verbs no doubt arise, but when a noun is a verb then come special state has been achieved. One of us must be speaking like: "Did you axe the tree down or did you use a saw?" and the other: " "I did saw the tree down." "Well, was your did a dud, or what?" Cunningly back "What I did is done, and what I do is forever." Forever on the record are we here now. If I am so incoherent then why not just come out with a few simple statements of the difference between operators and values? I suppose you could ask: "Can the operator be discussed without the values?", and I might quip: "Can the values be discussed without operators?" and it seems that the latter can hold down to counting. And yet denying counting is like denying material. If you wish to preach an immaterial mathematics then please be my guest. I will stay with material mathematics. Indeed the physicists' way is the material way, and it is that way which I have argued for. The rational value as philosophically pure may be had as a stage, and yet it may as well be absorbed into a previous stage at which point its purity is irrelevant. Indeed its impurity stands amplified under the scrutiny. Claiming that one value is composed of two values is about as foolhardy a construction as I can conceive. The notion of an element, and this in your set theory that you seem to think will strengthen your argument... Honestly I have attempted a cleaner form by dodging the set theory I think. Is 'three' one value or two values or three values? five values?
> > >>> I will provide you correct thinking on this at a later time.
> > >>> If you like all of these then I have a problem with your thinking. All of those things which are equivalent to three contain operators, and until they
> > >>> are solved there is no three. Should I try
> > >>>> 6 + 2 = 3 ?
> > >>>> 5 - 4 = 3 ?
> > >>>> 1 + 2 = 3 ?
> > >>>> It's pretty clear which side of the equation is simpler. Possibly if you found an even simpler form then you'd be onto an argument. Really, simplicity is on my side so strongly here that I feel entitled to print up all this rhetoric. All the valid formulations of three in the world are quite a plurality and if you'd like to start stating them in a long list I'm pretty sure you could do it here on USENET. That is how uncensored this medium is. I'm pretty sure that if I tried to have this conversation over on stack exchange I'd be halted by the censors. Math as religion there.
> > >>>>
> > >>>> The preposition seems a bit much to interject here, but because I am suffering this grammatical appropriateness it has to be said:
> > >>>> "A preposition is a word or group of words used before a noun, pronoun, or noun phrase to show direction, time, place, location, spatial relationships, or to introduce an object. Some examples of prepositions are words like "in," "at," "on," "of," and "to." "
> > >>>> - https://academicguides.waldenu.edu/writingcenter/grammar/prepositions
> > >>>>
> > >>>>
> > >>> that is Engrlish, not math, this is sci.math.
> > >
> > > The mathematician as information analyst may be a worthy discussion here. It fits my mantra that the divorced topics and their devorcees are practicing a lie. There is no divorce in a unified system. Unity is what we seek. Unification is correct. All z in polysign can take the Unitized() form. All that is needed is a magnitudinal component out front and we can work all z in general dimension on unit shells. Their character is in their angular behaviors, and now it is possible to claim polysign as a source of orthogonality which naturally unfolds from the preexisting simplex balance. The simplex balance is already in use within standard mathematics however it is not generally regarded as a modulo two system, or more properly a modulo 11 system. I do not mean your decimal eleven here, and I would think that any good information analyst could at least admit this simple detail without scrutiny. Nextly why have they not generalized nor even considered the modulo 111 system? Clearly their brights have not been on. Look at how many of them there are as well... and I a simpleton break into general dimensional algebra merely by this option. Really, you ought to be ashmed of yourself, Z.
> > >
> > that only makes sense if you use Mod0 math and transcribe using ascii II
> For the signature we've settiled in ASCII @ - + * # & ??? (these ellipsis of the unknown perfect for a budding mathematics)
> and this lowest @ symbol is intended to represent zero, and yet a double zero it possibly is. This would depend upon where you put your wrapping position. We have to confess that P16 is not really necessarily a fair depiction given the stricture that is occurring. Thus we can improve our purity by discussing
> P1111111111111111
> and now you can really count yourself lucky while working in Pn.
> There are not actually any subsettings happening here. It's just that the kaleidoscopic rotational results are trouble to our understanding. The complex rings are readily exposed from within polysign:
> https://drive.google.com/file/d/1UF1pum8eLOR09jTIpt3GdMZlgxYiH5zR/view?usp=sharing
> Oddly too, the embedded P3 rings are definable from a singular vector in Pn. We are spec'ing a plane through a vector due to the powers of that vector in the native space. This is the cause of the effect. That we keep seeing modulo three behaviors in all the superspaces, a bifurcation of the evens and odds and the EP2MU which under a fourth root masquerade as Ep3mu (tense change here; for now I like this better.) Also the pu is another mu within the embedded notation. The finder can filter these out, but the results are arbitrary. Either order may be opted for the sake of the analysis. If some compelling RHS versus LHS system guidance could be found polysign could be corrected to that form, but I'm not aware of any need to trouble over this symmetry. It existed in the complex plane as well.
>
> Forthcoming I'll simply label the graphic above with these coordinates. This could be a substantial graphic to some. It's a nice proof.
> Orthogonality arrives here as well. It's only predecessor would be Pn in high n, but these effects are coming out down low. These rings literally dominate under the self product, and really at random, as proven in the above graphic, the overwhelming majority of positions land themselves planar and fairly distributed. As well we are witnessing a magnitudinal growth factor with the signature based on powers of unit vectors out merely to four powers zzzz. It's causing me to go back to
> http://bandtechnology.com/PolySigned/MagnitudeAnalysis.html
> but the values are not lining up.
> There is always the possibility of a bug, and then too that data did nothing about getting onto a ring. The math now is on the rings that is coming to the clean figures. The latest data I guess it at the tail here.
>
>
> In CheckTheONEs
>
> EMU1: [P4 0.224144, 1.06066, 0.836516, 0 ]
> Error: 9.69969e-11
> Verified: EMU1^3 == ONE1 == ONE1*ONE1 (unitized)
> Nonunitized zzz (EMU) magnitude was 1.5
> Nonunitized zz (ONE) magnitude was 1.22474
> squared: 1.5
> ONE1: [P4 1.22474, 0.612372, 0, 0.612372 ]
>
> Sum of ONEs (EMUs^3): [P4 1.22474, 0.612372, 0, 0.612372 ]
>
>
> In CheckTheONEs
>
> EMU1: [P5 0.270481, 0, 0.494194, 1.0701, 0.931841 ]
> Error: 2.53382e-11
> Verified: EMU1^3 == ONE1 == ONE1*ONE1 (unitized)
> Nonunitized zzz (EMU) magnitude was 2
> Nonunitized zz (ONE) magnitude was 1.41421
> squared: 2
> ONE1: [P5 1.02333, 0.632456, 0, 1.08624e-12, 0.632456 ]
> EMU2: [P5 0.270481, 0.494194, 0.931841, 0, 1.0701 ]
> Error: 7.79318e-11
> Verified: EMU2^3 == ONE2 == ONE2*ONE2 (unitized)
> Nonunitized zzz (EMU) magnitude was 2
> Nonunitized zz (ONE) magnitude was 1.41421
> squared: 2
> ONE2: [P5 1.02333, 1.30795e-11, 0.632456, 0.632456, 0 ]
>
> Sum of ONEs (EMUs^3): [P5 1.41421, 1.6785e-11, 0, 2.22493e-11, 5.46363e-12 ]
>
>
> In CheckTheONEs
>
> EMU1: [P6 8.19541e-12, 0.790569, 0, 4.48791e-11, 0.790569, 3.66837e-11 ]
> Error: 5.10998e-11
> Verified: EMU1^3 == ONE1 == ONE1*ONE1 (unitized)
> Nonunitized zzz (EMU) magnitude was 2.5
> Nonunitized zz (ONE) magnitude was 1.58114
> squared: 2.5
> ONE1: [P6 0.790569, 0, 2.45862e-11, 0.790569, 0, 2.45862e-11 ]
> EMU2: [P6 0.263523, 0.790569, 1.05409, 0.790569, 0.263523, 0 ]
> Error: 3.68815e-11
> Verified: EMU2^3 == ONE2 == ONE2*ONE2 (unitized)
> Nonunitized zzz (EMU) magnitude was 2.5
> Nonunitized zz (ONE) magnitude was 1.58114
> squared: 2.5
> ONE2: [P6 1.05409, 0.790569, 0.263523, 0, 0.263523, 0.790569 ]
>
> Sum of ONEs (EMUs^3): [P6 1.58114, 0.527046, 3.06551e-11, 0.527046, 0, 0.527046 ]
>
>
> In CheckTheONEs
>
> EMU1: [P7 0.241909, 0, 0.126578, 0.526326, 0.898227, 0.96223, 0.670141 ]
> Error: 4.30175e-11
> Verified: EMU1^3 == ONE1 == ONE1*ONE1 (unitized)
> Nonunitized zzz (EMU) magnitude was 3
> Nonunitized zz (ONE) magnitude was 1.73205
> squared: 3
> ONE1: [P7 0.940736, 0.754411, 0.335745, 3.90576e-12, 0, 0.335745, 0.754411 ]
> EMU2: [P7 0.241909, 0.96223, 0.526326, 0, 0.670141, 0.898227, 0.126578 ]
> Error: 1.29158e-11
> Verified: EMU2^3 == ONE2 == ONE2*ONE2 (unitized)
> Nonunitized zzz (EMU) magnitude was 3
> Nonunitized zz (ONE) magnitude was 1.73205
> squared: 3
> ONE2: [P7 0.940736, 0.335745, 0, 0.754411, 0.754411, 7.66054e-14, 0.335745 ]
> EMU3: [P7 0.241909, 0.526326, 0.670141, 0.126578, 0.96223, 0, 0.898227 ]
> Error: 3.30493e-11
> Verified: EMU3^3 == ONE3 == ONE3*ONE3 (unitized)
> Nonunitized zzz (EMU) magnitude was 3
> Nonunitized zz (ONE) magnitude was 1.73205
> squared: 3
> ONE3: [P7 0.940736, 1.23279e-12, 0.754411, 0.335745, 0.335745, 0.754411, 0 ]
>
> Sum of ONEs (EMUs^3): [P7 1.73205, 8.44347e-12, 7.45981e-12, 7.49001e-12, 9.51905e-13, 9.82547e-13, 0 ]
>
>
> In CheckTheONEs
>
> EMU1: [P8 0.217917, 0.572822, 0.856817, 0.903541, 0.685624, 0.330719, 0.0467241, 0 ]
> Error: 5.50984e-11
> Verified: EMU1^3 == ONE1 == ONE1*ONE1 (unitized)
> Nonunitized zzz (EMU) magnitude was 3.5
> Nonunitized zz (ONE) magnitude was 1.87083
> squared: 3.5
> ONE1: [P8 0.935414, 0.798426, 0.467707, 0.136988, 0, 0.136988, 0.467707, 0.798426 ]
> EMU2: [P8 0.171193, 0, 0.6389, 0.810093, 0.171193, 1.14983e-11, 0.6389, 0.810093 ]
> Error: 2.36212e-11
> Verified: EMU2^3 == ONE2 == ONE2*ONE2 (unitized)
> Nonunitized zzz (EMU) magnitude was 3.5
> Nonunitized zz (ONE) magnitude was 1.87083
> squared: 3.5
> ONE2: [P8 0.935414, 0.467707, 0, 0.467707, 0.935414, 0.467707, 0, 0.467707 ]
> EMU3: [P8 0.217917, 0.903541, 0.0467241, 0.572822, 0.685624, 0, 0.856817, 0.330719 ]
> Error: 7.59919e-11
> Verified: EMU3^3 == ONE3 == ONE3*ONE3 (unitized)
> Nonunitized zzz (EMU) magnitude was 3.5
> Nonunitized zz (ONE) magnitude was 1.87083
> squared: 3.5
> ONE3: [P8 0.935414, 0.136988, 0.467707, 0.798426, 0, 0.798426, 0.467707, 0.136988 ]
>
> Sum of ONEs (EMUs^3): [P8 1.87083, 0.467707, 9.29101e-12, 0.467707, 4.64528e-12, 0.467707, 0, 0.467707 ]
>
>
> In CheckTheONEs
>
> EMU1: [P9 4.28772e-11, 0.666667, 8.48234e-11, 1.46027e-11, 0.666667, 5.16988e-25, 1.46027e-11, 0.666667, 0 ]
> Error: 7.96494e-11
> Verified: EMU1^3 == ONE1 == ONE1*ONE1 (unitized)
> Nonunitized zzz (EMU) magnitude was 4
> Nonunitized zz (ONE) magnitude was 2
> squared: 4
> ONE1: [P9 0.666667, 1.27408e-11, 1.29247e-26, 0.666667, 1.27408e-11, 0, 0.666667, 1.27408e-11, 1.29247e-26 ]
> EMU2: [P9 0.195419, 0, 3.8191e-12, 0.195419, 0.494818, 0.758105, 0.862086, 0.758105, 0.494818 ]
> Error: 3.77875e-11
> Verified: EMU2^3 == ONE2 == ONE2*ONE2 (unitized)
> Nonunitized zzz (EMU) magnitude was 4
> Nonunitized zz (ONE) magnitude was 2
> squared: 4
> ONE2: [P9 0.862086, 0.758105, 0.494818, 0.195419, 0, 1.08336e-12, 0.195419, 0.494818, 0.758105 ]
> EMU3: [P9 0.195419, 0, 0.494818, 0.862086, 0.494818, 2.2852e-12, 0.195419, 0.758105, 0.758105 ]
> Error: 1.63751e-11
> Verified: EMU3^3 == ONE3 == ONE3*ONE3 (unitized)
> Nonunitized zzz (EMU) magnitude was 4
> Nonunitized zz (ONE) magnitude was 2
> squared: 4
> ONE3: [P9 0.862086, 0.494818, 0, 0.195419, 0.758105, 0.758105, 0.195419, 7.45848e-13, 0.494818 ]
> EMU4: [P9 0.195419, 0.758105, 0, 0.862086, 3.02225e-12, 0.758105, 0.195419, 0.494818, 0.494818 ]
> Error: 6.15443e-11
> Verified: EMU4^3 == ONE4 == ONE4*ONE4 (unitized)
> Nonunitized zzz (EMU) magnitude was 4
> Nonunitized zz (ONE) magnitude was 2
> squared: 4
> ONE4: [P9 0.862086, 2.85749e-12, 0.758105, 0.195419, 0.494818, 0.494818, 0.195419, 0.758105, 0 ]
>
> Sum of ONEs (EMUs^3): [P9 2, 1.66946e-11, 0, 1.41787e-11, 1.34042e-11, 8.57203e-12, 7.79687e-12, 2.19769e-11, 5.28089e-12 ]
>
>
> In CheckTheONEs
>
> EMU1: [P10 0.202861, 0.0274084, 0, 0.131105, 0.370645, 0.627125, 0.802577, 0.829986, 0.698881, 0.459341 ]
> Error: 6.98756e-11
> Verified: EMU1^3 == ONE1 == ONE1*ONE1 (unitized)
> Nonunitized zzz (EMU) magnitude was 4.5
> Nonunitized zz (ONE) magnitude was 2.12132
> squared: 4.5
> ONE1: [P10 0.848528, 0.767501, 0.555369, 0.293159, 0.0810272, 0, 0.0810272, 0.293159, 0.555369, 0.767501 ]
> EMU2: [P10 0.202861, 0, 0.370645, 0.802577, 0.698881, 0.202861, 0, 0.370645, 0.802577, 0.698881 ]
> Error: 4.89003e-11
> Verified: EMU2^3 == ONE2 == ONE2*ONE2 (unitized)
> Nonunitized zzz (EMU) magnitude was 4.5
> Nonunitized zz (ONE) magnitude was 2.12132
> squared: 4.5
> ONE2: [P10 0.767501, 0.474342, 0, 3.65596e-12, 0.474342, 0.767501, 0.474342, 0, 3.65596e-12, 0.474342 ]
> EMU3: [P10 0.202861, 0.370645, 0.698881, 0, 0.802577, 0.202861, 0.370645, 0.698881, 0, 0.802577 ]
> Error: 1.8154e-11
> Verified: EMU3^3 == ONE3 == ONE3*ONE3 (unitized)
> Nonunitized zzz (EMU) magnitude was 4.5
> Nonunitized zz (ONE) magnitude was 2.12132
> squared: 4.5
> ONE3: [P10 0.767501, 0, 0.474342, 0.474342, 7.64189e-12, 0.767501, 0, 0.474342, 0.474342, 7.64189e-12 ]
> EMU4: [P10 0.202861, 0.829986, 0.370645, 0.0274084, 0.698881, 0.627125, 0, 0.459341, 0.802577, 0.131105 ]
> Error: 7.46484e-11
> Verified: EMU4^3 == ONE4 == ONE4*ONE4 (unitized)
> Nonunitized zzz (EMU) magnitude was 4.5
> Nonunitized zz (ONE) magnitude was 2.12132
> squared: 4.5
> ONE4: [P10 0.848528, 0.293159, 0.0810272, 0.767501, 0.555369, 0, 0.555369, 0.767501, 0.0810272, 0.293159 ]
>
> Sum of ONEs (EMUs^3): [P10 2.12132, 0.424264, 0, 0.424264, 5.44809e-12, 0.424264, 3.40616e-12, 0.424264, 8.85447e-12, 0.424264 ]
>
>
> In CheckTheONEs
>
> EMU1: [P11 0.201438, 0.782152, 0.500567, 0, 0.424062, 0.803928, 0.271745, 0.0433539, 0.640544, 0.698957, 0.0851409 ]
> Error: 9.61243e-11
> Verified: EMU1^3 == ONE1 == ONE1*ONE1 (unitized)
> Nonunitized zzz (EMU) magnitude was 5
> Nonunitized zz (ONE) magnitude was 2.23607
> squared: 5
> ONE1: [P11 0.796647, 0.33223, 0, 0.55898, 0.732108, 0.123851, 0.123851, 0.732108, 0.55898, 2.33147e-14, 0.33223 ]
> EMU2: [P11 0.201438, 0.0433539, 0, 0.0851409, 0.271745, 0.500567, 0.698957, 0.803928, 0.782152, 0.640544, 0.424062 ]
> Error: 8.28956e-11
> Verified: EMU2^3 == ONE2 == ONE2*ONE2 (unitized)
> Nonunitized zzz (EMU) magnitude was 5
> Nonunitized zz (ONE) magnitude was 2.23607
> squared: 5
> ONE2: [P11 0.796647, 0.732108, 0.55898, 0.33223, 0.123851, 4.71401e-12, 0, 0.123851, 0.33223, 0.55898, 0.732108 ]
> EMU3: [P11 0.201438, 0.698957, 0.0433539, 0.803928, 0, 0.782152, 0.0851409, 0.640544, 0.271745, 0.424062, 0.500567 ]
> Error: 5.82021e-11
> Verified: EMU3^3 == ONE3 == ONE3*ONE3 (unitized)
> Nonunitized zzz (EMU) magnitude was 5
> Nonunitized zz (ONE) magnitude was 2.23607
> squared: 5
> ONE3: [P11 0.796647, 1.88272e-12, 0.732108, 0.123851, 0.55898, 0.33223, 0.33223, 0.55898, 0.123851, 0.732108, 0 ]
> EMU4: [P11 0.201438, 0, 0.271745, 0.698957, 0.782152, 0.424062, 0.0433539, 0.0851409, 0.500567, 0.803928, 0.640544 ]
> Error: 9.89181e-11
> Verified: EMU4^3 == ONE4 == ONE4*ONE4 (unitized)
> Nonunitized zzz (EMU) magnitude was 5
> Nonunitized zz (ONE) magnitude was 2.23607
> squared: 5
> ONE4: [P11 0.796647, 0.55898, 0.123851, 2.09455e-12, 0.33223, 0.732108, 0.732108, 0.33223, 0, 0.123851, 0.55898 ]
> EMU5: [P11 0.201438, 0.803928, 0.0851409, 0.424062, 0.698957, 0, 0.640544, 0.500567, 0.0433539, 0.782152, 0.271745 ]
> Error: 2.90418e-11
> Verified: EMU5^3 == ONE5 == ONE5*ONE5 (unitized)
> Nonunitized zzz (EMU) magnitude was 5
> Nonunitized zz (ONE) magnitude was 2.23607
> squared: 5
> ONE5: [P11 0.796647, 0.123851, 0.33223, 0.732108, 0, 0.55898, 0.55898, 1.09956e-12, 0.732108, 0.33223, 0.123851 ]
>
> Sum of ONEs (EMUs^3): [P11 2.23607, 1.14089e-11, 1.56746e-11, 2.15221e-11, 1.71956e-11, 2.02407e-11, 1.28009e-12, 4.32521e-12, 0, 5.84599e-12, 1.01117e-11 ]
>
>
> In CheckTheONEs
>
> EMU1: [P12 0.195434, 0.72937, 0, 0.72937, 0.195434, 0.390868, 0.586302, 0.0523664, 0.781736, 0.0523664, 0.586302, 0.390868 ]
> Error: 4.2193e-11
> Verified: EMU1^3 == ONE1 == ONE1*ONE1 (unitized)
> Nonunitized zzz (EMU) magnitude was 5.5
> Nonunitized zz (ONE) magnitude was 2.34521
> squared: 5.5
> ONE1: [P12 0.781736, 0.0523664, 0.586302, 0.390868, 0.195434, 0.72937, 0, 0.72937, 0.195434, 0.390868, 0.586302, 0.0523664 ]
> EMU2: [P12 0.195434, 0, 0.195434, 0.586302, 0.781736, 0.586302, 0.195434, 4.68375e-17, 0.195434, 0.586302, 0.781736, 0.586302 ]
> Error: 9.64404e-11
> Verified: EMU2^3 == ONE2 == ONE2*ONE2 (unitized)
> Nonunitized zzz (EMU) magnitude was 5.5
> Nonunitized zz (ONE) magnitude was 2.34521
> squared: 5.5
> ONE2: [P12 0.781736, 0.586302, 0.195434, 0, 0.195434, 0.586302, 0.781736, 0.586302, 0.195434, 0, 0.195434, 0.586302 ]
> EMU3: [P12 0.143068, 0.677003, 0.533936, 0, 0.143068, 0.677003, 0.533936, 0, 0.143068, 0.677003, 0.533936, 0 ]
> Error: 4.84322e-11
> Verified: EMU3^3 == ONE3 == ONE3*ONE3 (unitized)
> Nonunitized zzz (EMU) magnitude was 5.5
> Nonunitized zz (ONE) magnitude was 2.34521
> squared: 5.5
> ONE3: [P12 0.781736, 0.390868, 0, 0.390868, 0.781736, 0.390868, 0, 0.390868, 0.781736, 0.390868, 0, 0.390868 ]
> EMU4: [P12 3.64121e-11, 4.67191e-12, 0.586302, 0, 1.19543e-11, 0.586302, 0, 4.67191e-12, 0.586302, 0, 1.19543e-11, 0.586302 ]
> Error: 3.48024e-11
> Verified: EMU4^3 == ONE4 == ONE4*ONE4 (unitized)
> Nonunitized zzz (EMU) magnitude was 5.5
> Nonunitized zz (ONE) magnitude was 2.34521
> squared: 5.5
> ONE4: [P12 0.586302, 2.3697e-12, 0, 0.586302, 2.3697e-12, 0, 0.586302, 2.3697e-12, 0, 0.586302, 2.3697e-12, 0 ]
> EMU5: [P12 0.195434, 0.0523664, 0, 0.0523664, 0.195434, 0.390868, 0.586302, 0.72937, 0.781736, 0.72937, 0.586302, 0.390868 ]
> Error: 6.34729e-11
> Verified: EMU5^3 == ONE5 == ONE5*ONE5 (unitized)
> Nonunitized zzz (EMU) magnitude was 5.5
> Nonunitized zz (ONE) magnitude was 2.34521
> squared: 5.5
> ONE5: [P12 0.781736, 0.72937, 0.586302, 0.390868, 0.195434, 0.0523664, 0, 0.0523664, 0.195434, 0.390868, 0.586302, 0.72937 ]
>
> Sum of ONEs (EMUs^3): [P12 2.34521, 0.390868, 0, 0.390868, 1.24349e-11, 0.390868, 8.81584e-12, 0.390868, 5.1954e-12, 0.390868, 1.76308e-11, 0.390868 ]
>
>
> In CheckTheONEs
>
> EMU1: [P13 0.1872, 0.360449, 0.537173, 0.676888, 0.747587, 0.733073, 0.636672, 0.480467, 0.300244, 0.137289, 0.0289333, 0, 0.0571173 ]
> Error: 4.37606e-11
> Verified: EMU1^3 == ONE1 == ONE1*ONE1 (unitized)
> Nonunitized zzz (EMU) magnitude was 6
> Nonunitized zz (ONE) magnitude was 2.44949
> squared: 6
> ONE1: [P13 0.742739, 0.699573, 0.579966, 0.411318, 0.232263, 0.0838219, 0, 6.84786e-13, 0.0838219, 0.232263, 0.411318, 0.579966, 0.699573 ]
> EMU2: [P13 0.1872, 0.300244, 0.676888, 0, 0.636672, 0.360449, 0.137289, 0.747587, 0.0571173, 0.480467, 0.537173, 0.0289333, 0.733073 ]
> Error: 5.53374e-11
> Verified: EMU2^3 == ONE2 == ONE2*ONE2 (unitized)
> Nonunitized zzz (EMU) magnitude was 6
> Nonunitized zz (ONE) magnitude was 2.44949
> squared: 6
> ONE2: [P13 0.742739, 0.0838219, 0.411318, 0.579966, 2.3801e-12, 0.699573, 0.232263, 0.232263, 0.699573, 0, 0.579966, 0.411318, 0.0838219 ]
> EMU3: [P13 0.1872, 0.636672, 0.0571173, 0.733073, 0, 0.747587, 0.0289333, 0.676888, 0.137289, 0.537173, 0.300244, 0.360449, 0.480467 ]
> Error: 3.88203e-11
> Verified: EMU3^3 == ONE3 == ONE3*ONE3 (unitized)
> Nonunitized zzz (EMU) magnitude was 6
> Nonunitized zz (ONE) magnitude was 2.44949
> squared: 6
> ONE3: [P13 0.742739, 5.32685e-13, 0.699573, 0.0838219, 0.579966, 0.232263, 0.411318, 0.411318, 0.232263, 0.579966, 0.0838219, 0.699573, 0 ]
> EMU4: [P13 0.1872, 0, 0.137289, 0.480467, 0.733073, 0.676888, 0.360449, 0.0571173, 0.0289333, 0.300244, 0.636672, 0.747587, 0.537173 ]
> Error: 3.14432e-11
> Verified: EMU4^3 == ONE4 == ONE4*ONE4 (unitized)
> Nonunitized zzz (EMU) magnitude was 6
> Nonunitized zz (ONE) magnitude was 2.44949
> squared: 6
> ONE4: [P13 0.742739, 0.579966, 0.232263, 0, 0.0838219, 0.411318, 0.699573, 0.699573, 0.411318, 0.0838219, 3.63265e-13, 0.232263, 0.579966 ]
> EMU5: [P13 0.1872, 0.0289333, 0.480467, 0.747587, 0.360449, 0, 0.300244, 0.733073, 0.537173, 0.0571173, 0.137289, 0.636672, 0.676888 ]
> Error: 4.78371e-11
> Verified: EMU5^3 == ONE5 == ONE5*ONE5 (unitized)
> Nonunitized zzz (EMU) magnitude was 6
> Nonunitized zz (ONE) magnitude was 2.44949
> squared: 6
> ONE5: [P13 0.742739, 0.411318, 0, 0.232263, 0.699573, 0.579966, 0.0838219, 0.0838219, 0.579966, 0.699573, 0.232263, 5.11147e-13, 0.411318 ]
> EMU6: [P13 0.1872, 0.747587, 0.300244, 0.0571173, 0.676888, 0.480467, 0, 0.537173, 0.636672, 0.0289333, 0.360449, 0.733073, 0.137289 ]
> Error: 2.47023e-11
> Verified: EMU6^3 == ONE6 == ONE6*ONE6 (unitized)
> Nonunitized zzz (EMU) magnitude was 6
> Nonunitized zz (ONE) magnitude was 2.44949
> squared: 6
> ONE6: [P13 0.742739, 0.232263, 0.0838219, 0.699573, 0.411318, 0, 0.579966, 0.579966, 2.14717e-13, 0.411318, 0.699573, 0.0838219, 0.232263 ]
>
> Sum of ONEs (EMUs^3): [P13 2.44949, 1.8594e-12, 8.8014e-12, 2.65343e-12, 7.20268e-12, 8.9897e-12, 0, 1.36411e-11, 4.65272e-12, 6.44018e-12, 1.09881e-11, 4.84102e-12, 1.17821e-11 ]
>
>
> In CheckTheONEs
>
> EMU1: [P14 0.17804, 0.227085, 0.708182, 0.0592186, 0.387366, 0.627137, 0, 0.542256, 0.493211, 0.0121131, 0.661077, 0.33293, 0.0931587, 0.720295 ]
> Error: 5.49482e-11
> Verified: EMU1^3 == ONE1 == ONE1*ONE1 (unitized)
> Nonunitized zzz (EMU) magnitude was 6.5
> Nonunitized zz (ONE) magnitude was 2.54951
> squared: 6.5
> ONE1: [P14 0.728431, 0.137131, 0.28317, 0.692363, 0.0360687, 0.445261, 0.5913, 0, 0.5913, 0.445261, 0.0360687, 0.692363, 0.28317, 0.137131 ]
> EMU2: [P14 0.17804, 0, 0.0931587, 0.387366, 0.661077, 0.708182, 0.493211, 0.17804, 0, 0.0931587, 0.387366, 0.661077, 0.708182, 0.493211 ]
> Error: 5.01628e-11
> Verified: EMU2^3 == ONE2 == ONE2*ONE2 (unitized)
> Nonunitized zzz (EMU) magnitude was 6.5
> Nonunitized zz (ONE) magnitude was 2.54951
> squared: 6.5
> ONE2: [P14 0.692363, 0.555232, 0.247101, 6.10401e-13, 0, 0.247101, 0.555232, 0.692363, 0.555232, 0.247101, 6.10401e-13, 0, 0.247101, 0.555232 ]
> EMU3: [P14 0.17804, 0.387366, 0.493211, 0.0931587, 0.708182, 0, 0.661077, 0.17804, 0.387366, 0.493211, 0.0931587, 0.708182, 0, 0.661077 ]
> Error: 6.31541e-11
> Verified: EMU3^3 == ONE3 == ONE3*ONE3 (unitized)
> Nonunitized zzz (EMU) magnitude was 6.5
> Nonunitized zz (ONE) magnitude was 2.54951
> squared: 6.5
> ONE3: [P14 0.692363, 0, 0.555232, 0.247101, 0.247101, 0.555232, 4.4782e-12, 0.692363, 2.22045e-16, 0.555232, 0.247101, 0.247101, 0.555232, 4.4782e-12 ]
> EMU4: [P14 0.17804, 0.0121131, 0.387366, 0.720295, 0.493211, 0.0592186, 0.0931587, 0.542256, 0.708182, 0.33293, 0, 0.227085, 0.661077, 0.627137 ]
> Error: 6.49721e-11
> Verified: EMU4^3 == ONE4 == ONE4*ONE4 (unitized)
> Nonunitized zzz (EMU) magnitude was 6.5
> Nonunitized zz (ONE) magnitude was 2.54951
> squared: 6.5
> ONE4: [P14 0.728431, 0.445261, 0.0360687, 0.137131, 0.5913, 0.692363, 0.28317, 0, 0.28317, 0.692363, 0.5913, 0.137131, 0.0360687, 0.445261 ]
> EMU5: [P14 0.17804, 0.708182, 0.387366, 0, 0.493211, 0.661077, 0.0931587, 0.17804, 0.708182, 0.387366, 0, 0.493211, 0.661077, 0.0931587 ]
> Error: 9.69908e-11
> Verified: EMU5^3 == ONE5 == ONE5*ONE5 (unitized)
> Nonunitized zzz (EMU) magnitude was 6.5
> Nonunitized zz (ONE) magnitude was 2.54951
> squared: 6.5
> ONE5: [P14 0.692363, 0.247101, 5.79581e-12, 0.555232, 0.555232, 0, 0.247101, 0.692363, 0.247101, 5.79603e-12, 0.555232, 0.555232, 2.22045e-16, 0.247101 ]
> EMU6: [P14 0.17804, 0.33293, 0.493211, 0.627137, 0.708182, 0.720295, 0.661077, 0.542256, 0.387366, 0.227085, 0.0931587, 0.0121131, 0, 0.0592186 ]
> Error: 7.42616e-11
> Verified: EMU6^3 == ONE6 == ONE6*ONE6 (unitized)
> Nonunitized zzz (EMU) magnitude was 6.5
> Nonunitized zz (ONE) magnitude was 2.54951
> squared: 6.5
> ONE6: [P14 0.728431, 0.692363, 0.5913, 0.445261, 0.28317, 0.137131, 0.0360687, 0, 0.0360687, 0.137131, 0.28317, 0.445261, 0.5913, 0.692363 ]
>
> Sum of ONEs (EMUs^3): [P14 2.54951, 0.364216, 2.24927e-11, 0.364216, 1.64371e-11, 0.364216, 1.64608e-11, 0.364216, 6.03184e-12, 0.364216, 6.05671e-12, 0.364216, 0, 0.364216 ]
>
>
> In CheckTheONEs
>
> EMU1: [P15 0.168675, 0.0596637, 0.581105, 0.581105, 0.0596637, 0.168675, 0.667327, 0.454069, 0, 0.308184, 0.697825, 0.308184, 1.08982e-11, 0.454069, 0.667327 ]
> Error: 8.10427e-11
> Verified: EMU1^3 == ONE1 == ONE1*ONE1 (unitized)
> Nonunitized zzz (EMU) magnitude was 7
> Nonunitized zz (ONE) magnitude was 2.64575
> squared: 7
> ONE1: [P15 0.697825, 0.308184, 0, 0.454069, 0.667327, 0.168675, 0.0596637, 0.581105, 0.581105, 0.0596637, 0.168675, 0.667327, 0.454069, 3.64708e-13, 0.308184 ]
> EMU2: [P15 0.168675, 0.0596637, 6.16075e-11, 0, 0.0596637, 0.168675, 0.308184, 0.454069, 0.581105, 0.667327, 0.697825, 0.667327, 0.581105, 0.454069, 0.308184 ]
> Error: 7.89257e-11
> Verified: EMU2^3 == ONE2 == ONE2*ONE2 (unitized)
> Nonunitized zzz (EMU) magnitude was 7
> Nonunitized zz (ONE) magnitude was 2.64575
> squared: 7
> ONE2: [P15 0.697825, 0.667327, 0.581105, 0.454069, 0.308184, 0.168675, 0.0596637, 0, 1.23235e-12, 0.0596637, 0.168675, 0.308184, 0.454069, 0.581105, 0.667327 ]
> EMU3: [P15 0.168675, 0.308184, 0.581105, 0, 0.667327, 0.168675, 0.308184, 0.581105, 9.81554e-12, 0.667327, 0.168675, 0.308184, 0.581105, 1.99952e-12, 0.667327 ]
> Error: 8.78221e-11
> Verified: EMU3^3 == ONE3 == ONE3*ONE3 (unitized)
> Nonunitized zzz (EMU) magnitude was 7
> Nonunitized zz (ONE) magnitude was 2.64575
> squared: 7
> ONE3: [P15 0.638161, 4.44089e-16, 0.394405, 0.394405, 5.66214e-13, 0.638161, 4.44089e-16, 0.394405, 0.394405, 5.66214e-13, 0.638161, 0, 0.394405, 0.394405, 5.66214e-13 ]
> EMU4: [P15 0.168675, 0.581105, 0.667327, 0.308184, 0, 0.168675, 0.581105, 0.667327, 0.308184, 0, 0.168675, 0.581105, 0.667327, 0.308184, 0 ]
> Error: 4.62809e-11
> Verified: EMU4^3 == ONE4 == ONE4*ONE4 (unitized)
> Nonunitized zzz (EMU) magnitude was 7
> Nonunitized zz (ONE) magnitude was 2.64575
> squared: 7
> ONE4: [P15 0.638161, 0.394405, 2.87637e-12, 2.22045e-16, 0.394405, 0.638161, 0.394405, 2.87637e-12, 0, 0.394405, 0.638161, 0.394405, 2.87614e-12, 2.22045e-16, 0.394405 ]
> EMU5: [P15 3.46964e-12, 3.24255e-22, 0.52915, 3.46964e-12, 3.52379e-22, 0.52915, 3.46964e-12, 0, 0.52915, 3.46964e-12, 1.10465e-19, 0.52915, 3.46964e-12, 1.69407e-21, 0.52915 ]
> Error: 2.19589e-11
> Verified: EMU5^3 == ONE5 == ONE5*ONE5 (unitized)
> Nonunitized zzz (EMU) magnitude was 7
> Nonunitized zz (ONE) magnitude was 2.64575
> squared: 7
> ONE5: [P15 0.52915, 1.04089e-11, 2.40741e-35, 0.52915, 1.04089e-11, 0, 0.52915, 1.04089e-11, 2.40741e-35, 0.52915, 1.04089e-11, 2.40741e-35, 0.52915, 1.04089e-11, 0 ]
> EMU6: [P15 0.168675, 0.581105, 0.0596637, 0.667327, 2.6567e-11, 0.697825, 0, 0.667327, 0.0596637, 0.581105, 0.168675, 0.454069, 0.308184, 0.308184, 0.454069 ]
> Error: 3.61767e-11
> Verified: EMU6^3 == ONE6 == ONE6*ONE6 (unitized)
> Nonunitized zzz (EMU) magnitude was 7
> Nonunitized zz (ONE) magnitude was 2.64575
> squared: 7
> ONE6: [P15 0.697825, 0, 0.667327, 0.0596637, 0.581105, 0.168675, 0.454069, 0.308184, 0.308184, 0.454069, 0.168675, 0.581105, 0.0596637, 0.667327, 4.51417e-13 ]
> EMU7: [P15 0.168675, 0.454069, 0.667327, 0.667327, 0.454069, 0.168675, 6.57904e-12, 0.0596637, 0.308184, 0.581105, 0.697825, 0.581105, 0.308184, 0.0596637, 0 ]
> Error: 6.09295e-11
> Verified: EMU7^3 == ONE7 == ONE7*ONE7 (unitized)
> Nonunitized zzz (EMU) magnitude was 7
> Nonunitized zz (ONE) magnitude was 2.64575
> squared: 7
> ONE7: [P15 0.697825, 0.581105, 0.308184, 0.0596637, 3.25517e-13, 0.168675, 0.454069, 0.667327, 0.667327, 0.454069, 0.168675, 0, 0.0596637, 0.308184, 0.581105 ]
>
> Sum of ONEs (EMUs^3): [P15 2.64575, 1.33826e-11, 1.24345e-12, 6.27942e-13, 8.81384e-12, 0, 8.83915e-12, 1.23452e-11, 2.20268e-12, 5.71143e-12, 1.45493e-11, 5.73586e-12, 1.39218e-11, 1.33045e-11, 1.16662e-12 ]

I'm afraid this data may be bad. I'm getting some terrible results right now.
I did change a few things around but have graphing going with the emus values and graphical locations.
Some of the emus are bad.

Anyway, the ume are neat in that while we are general dimensional, just one vector suffices to declare the plane that it is in. It is the product behavior itself that is under analysis and emu emu acts like emu does. Emu emu emu acts like NU. Emu acts like MU. Just emu is needed and the rest come along for free. The complex equivalent suggests that just the complex are i or -i (they are indistinguishable) are the next as pentamus. Under this language the first set are quadramus. Trimus, anyone? The lowly p2mu is the trimu. Bimu... z z = z... ahh.....

[yuuyyu]

Timothy Golden wrote:

>> Sum of ONEs (EMUs^3): [P15 2.64575, 1.33826e-11, 1.24345e-12,
>> 6.27942e-13, 8.81384e-12, 0, 8.83915e-12, 1.23452e-11, 2.20268e-12,
>> 5.71143e-12, 1.45493e-11, 5.73586e-12, 1.39218e-11, 1.33045e-11,
>> 1.16662e-12 ]
>
> I'm afraid this data may be bad. I'm getting some terrible results right
> now.

not matter, quote less, you moron. You just did 773 lines.

[Timothy Golden]

I like your short version.
(2.64575)(2.64575) = 7 = (n-1) / 2.
Strangely this factor is taken per product; not per value.

[Timothy Golden]

On Wednesday, November 10, 2021 at 9:39:48 AM UTC-5, Ross A. Finlayson wrote:

> On Monday, November 8, 2021 at 11:05:06 AM UTC-8, FromTheRafters wrote:
> > Ross A. Finlayson pretended :
> > > On Monday, November 8, 2021 at 6:14:06 AM UTC-8, FromTheRafters wrote:
> > >> Timothy Golden explained :
> > >>> "We make the set first, the operators after on the set."
> > >>> How strange it is then at the stage of developing the continuum that this
> > >>> rule was broken.
> > >> How was it broken? To me it was the lack of set closure of inverse
> > >> operators which made extension and embedding necessary.
> > >
> > > I thought he meant linear operators with respect to operator algebras.
> > I think he means anything that sheds light upon his notion that a/b in
> > Q should be interpreted and stated as two elements and an operator
> > rather than as a single symbol for an ordered pair <a,b> element in Q
> > where both a and b are also ordered pairs of N in Z.
> >
> > He seems to not like abstraction, but without it things get quite messy
> > very quickly.
> It seems like the usual abstraction of rationals is "real-values of reduced fractions",
> w.r.t. an algebra's field and the usual. Then, it seems that for augmenting the system
> where 3/2 and 6/4 are distinct, is about some matters of scale, that instead of the
> usual origin and the line that instead it's destination and bounds.

Or simply values along the way. This is the simplest way to witness these values; each in their own progression:
1.1 10.0 10.1 11.0 ... the halves continue this way.
1.2 1.3 2.0 2.1 ... and the quarters too.

Each to their own and then to the bunch. Isn't this how your addition is best performed?
Now as we speak of evaluation we really are merely shifting modulo levels. These cryptic values can take their rational form; fine. They likewise have this other primitive form. As to which is simpler I know you know how I feel about it. They only sum nicely when converted to another base. They don't do this well. The poor thirds in the base ten do suffer, we know. So just settle out a few digits and call it good till you can't call it good any more. Until then all is well. Out by a microthird? Nah, centithirds will do.

0.1b3 = 0.33bA

of dear I bumped into an aleph.

[zelos...@gmail.com]

>This I do think matters. I did scan your other posts and I see you are serious about staying on here.

I am very serious on showing you wrong.

>As to what is fundamental: isn't it true that what is simpler is more fundamental?

Nope.

>That 1.23 does not seem to describe any operator. It is purely value.

A lot of what you want to call operator is just an element.

>Here again I cannot claim to be fully in the clear,

You have never been in the clear on ANYTHING given you nSTILL work in high school territory of understanding!

>for these counting mechanisms in their own way carry ongoing zero exceptions. There is a little rod on the wheel of digits 1234567890 (these forming a ring already) which connects to teeth on the next digit up.

Skip all this radix shite, it is not relevant, it is just notation.

>Without this mechanism we cannot discuss the value 101.

we agree on decimal notation, get over it already.

>Come now, can't you see that the decimal point is merely a tacked on structure?

It isn't tact on structure, it is a defined NOTATION. The STRUCTURE is how the numbers work.

>Whereas the rational value requires two of the original value and an operator the decimal point is a different type.

False, rational NUMBERS have NO operator in them. [(a,b)] is not containing an operation!

>Obviously in our standard notation it is a little dot. And nicely enough we do not see any operator yet if we were to grant an operator to the decimal point it would be as a product relation; a fundamental operator.

Here we go again with you not fuckign understanding what an operator is, what an element is, how functions work or notation. You literally misunderstand EVERYTHING.

>So I believe that I have substantiated a strong difference and preference for 1.23 as more fundamental than 123/100.

No you haven't. One notation is not more fundamental than another. Notation is just for us humans to convey things and 1.23 is more CONVENIENT than 123/100. There is nothing "more fundamental" to either of them because they both refer to THE SAME OBJECT.

>And here we have returned around in circular fashion to our old discussion point where you claim that two values and an operator are one value,

No, I claim that an element is an element and you claim it isn't based on NOTATION ALONE!

f(x) is not "a function and an element", it is AN ELEMENT, the element gotten BY APPLYING THE FUNCTION f ON THE ELEMENT x!!!
Same is a/b=/(a,b) or a*b=*(a,b), they are ELEMENTS! Elements that the function binary functions / and * output when a and b are inputs!

>and I continue to hold my ground, though now my ground is a bit better footed on the argument I have just provided.

Nope, you are STILL just arguing based on notation which is FAULTY AND RETARDED! Learn mathematics and its foundations!

[zelos...@gmail.com]

>Z has done a good job exposing himself.

I do a good job exposing your stupidity :)

>He has claimed that the values must be built before the operators can be applied to them.

No, I claim that a set must be constructed first BEFORE you can define operators on it!

>If the rational values build a number system then he is caught denying that the division operator exists.

We define division on rational numbers AFTER we construct the rational numbers!

>This is not only Z's problem.

You have yet to demonstrate ANY problem that isn't based on your IGNORANCE!

>Z has started to substantiate operators on rationals that make addition look more complicated than division.

It is the way the construction of rational numbers go, educate yourself you retard.

[Timothy Golden]

On Thursday, November 11, 2021 at 1:08:19 AM UTC-5, zelos...@gmail.com wrote:
> >Z has done a good job exposing himself.
> I do a good job exposing your stupidity :)
> >He has claimed that the values must be built before the operators can be applied to them.
> No, I claim that a set must be constructed first BEFORE you can define operators on it!

I'm sorry, but I am attempting to pay attention to such falsifications, yet I see none here.
Our language is synonymous. So I must ask you to please point out what exactly in my language differs from your language.
It seems to me that we are in complete agreement here. This is good but as to why you've slipped in an inversion I have no idea.

> >If the rational values build a number system then he is caught denying that the division operator exists.
> We define division on rational numbers AFTER we construct the rational numbers!

Now this statement I do have a problem with. The rational numbers are not the rational numbers until we utter such things as:
1/3, 4/56, 7/8, etc.
Clearly the division symbol is within the rational value itself. I have no ability to utter a rational value without including the division symbol.

> >This is not only Z's problem.
> You have yet to demonstrate ANY problem that isn't based on your IGNORANCE!
> >Z has started to substantiate operators on rationals that make addition look more complicated than division.
> It is the way the construction of rational numbers go, educate yourself you retard.

I'm sorry, but the rational value without its division symbol is not the rational value. It's entire identity would be gone.
2/3 = 0.2b111 ~ 0.66b1111111111
That it can be evaluated is damning.
It's resolution to a single value is suggestive. I suppose you are fooling yourself into believing something that you were taught and has been taught for so many generations... except that we now arrive in a more formal system. Indeed, compiler level integrity was not a thing of the past. The compilers of the past merely had to say 'good enough'. The thing is that the sort of confusion that is taking place here is actually beyond a compiler error. Why? Because the very structure of operators and values are the lexicon of mathematics. The breakage is obvious for all to see once the melon is cracked. To expect that one as you, Z, could never find your way to challenging the status quo; yeah, you lack the integrity to do this. Your mind has been bent into shape already. As you negate our identical statements so that yours is true and mine is false I can't help but wonder whether your own melon is cracking? It is of course an appropriate point, especially if I am correct, and I suppose some readers are willing to at least put a foot in the doorway here, an appropriate point to consider political sway and possibly even some race theory within mathematics. to what degree can the European claim the decimal value even? He cannot. He must give that to Asia. The decimal point? Radix point is a better term, and yet unit point is even better. https://en.wikipedia.org/wiki/Decimal_separator

We see that many formats have been taken. What are their meanings? The language of the 'fractional part' still exists today. Yet, upon removing the decimal point we will see one integer value. The radix character of the digits is no different than the integer. The mechanics are built in. We all know it works. We know that there is a discrepancy between the mathematicians version of the number and the physicists version. I am wiping that clean here. When epsilon/delta applies to all values then we have the physicists version and we have universal values; not the hodge-podge of 'reals' and snarky math professors quipping on perfection. A bunch of clowns. Oh, you were serious? Seriously mimicking, sir.

[zelos...@gmail.com]

>I'm sorry, but I am attempting to pay attention to such falsifications, yet I see none here.
>Our language is synonymous.

Nope, yours entail the operator is defined already before the set, mine states that the operator is defined AFTER the set

>Now this statement I do have a problem with. The rational numbers are not the rational numbers until we utter such things as:

False, we do not need to utter anything. Rational numbers are defined as a field, the smallest non-finite field (if I recall correctly) we do not need any specific notation.

>1/3, 4/56, 7/8, etc.

Which is done for historical reasons instead of the proper construction of [(1,3)] [(4,56)], etc

>Clearly the division symbol is within the rational value itself. I have no ability to utter a rational value without including the division symbol.

The SYMBOL is there because of HISTORY but it is not DEFINED by it. We defined rational numbers in terms of equivalence classes of rational numbers [(a,b)] which we then choose to WRITE as a/b

>I'm sorry, but the rational value without its division symbol is not the rational value. It's entire identity would be gone.

False, the symbol is irrelevant to rational numbers.

Rational numbers is defined through field of fraction of integers
https://proofwiki.org/wiki/Definition:Field_of_Quotients
the symbol is irrelevant.

>That it can be evaluated is damning.

There is nothing to evaluate, but you need an evaluation to see how insane you are.

>It's resolution to a single value is suggestive.

What are you talking about here?

>I suppose you are fooling yourself into believing something that you were taught and has been taught for so many generations...

I am not fooled by anything, I understand how numbers are constructed and abstract algebra. Something you clearly do not.

>except that we now arrive in a more formal system.

Excuse me? Yours is NOT formal, what I tell you has FORMAL DEFINITIONS! FORMAL CONSTRUCTIONS and much else!
It is ALL formal but you are too STUPID to understand!

>Indeed, compiler level integrity was not a thing of the past. The compilers of the past merely had to say 'good enough'.

compilers are computers, irrelevant to mathematics.

>To expect that one as you, Z, could never find your way to challenging the status quo; yeah, you lack the integrity to do this.

There is no reason to challange this because we understand this extremely well. You cannot challenge it the way you want to because what you are doing is based on IGNORANCE.

>As you negate our identical statements so that yours is true and mine is false I can't help but wonder whether your own melon is cracking?

As I pointed out, there is a subtle difference.

>an appropriate point to consider political sway and possibly even some race theory within mathematics.

uh why? They are irrelevant in mathematics.

>to what degree can the European claim the decimal value even? He cannot. He must give that to Asia. The decimal point? Radix point is a better term, and yet unit point is even better. https://en.wikipedia.org/wiki/Decimal_separator

This is just notation, not interesting in mathematics.

>We know that there is a discrepancy between the mathematicians version of the number and the physicists version. I am wiping that clean here.

Is that what you want? to have it based on physics? That is not happening, mathematics has separated itself from physics and reality slowly but surely because the more we do it, the more POWERFUL it becomes and the more USEFUL it becomes. You are trying to make mathematics WEAKER.

>When epsilon/delta applies to all values then we have the physicists version and we have universal values; not the hodge-podge of 'reals' and snarky math professors quipping on perfection. A bunch of clowns. Oh, you were serious? Seriously mimicking, sir.

So you pretty much admit here that you hate it because it makes you feel stupid?

[Timothy Golden]

On Friday, November 12, 2021 at 4:17:03 AM UTC-5, zelos...@gmail.com wrote:
> >I'm sorry, but I am attempting to pay attention to such falsifications, yet I see none here.
> >Our language is synonymous.
> Nope, yours entail the operator is defined already before the set, mine states that the operator is defined AFTER the set

You've deleted the language and now I will put it back:
Here is my statement:

> >He has claimed that the values must be built before the operators can be applied to them.

And here is your first response:

> No, I claim that a set must be constructed first BEFORE you can define operators on it!

and it is obvious to any who read along that these statements are synonymous;
To which I say:

I'm sorry, but I am attempting to pay attention to such falsifications, yet I see none here.

Our language is synonymous. So I must ask you to please point out what exactly in my language differs from your language.
It seems to me that we are in complete agreement here. This is good but as to why you've slipped in an inversion I have no idea.

and you've falsely now claimed that I believe that "the operator is defined already before the set"

This is a fine instance of you, Zelos, failing to hold a clean discussion. This is quite a serious topic here and I pity anyone who holds the same side as you do.

I'd like to say that you are doing a fine job holding up the status quo, but this is not quite how I see it here. Your lame defense of the status quo... really my argument deserves better than you can give. Accountability is not your cup of tea.

The discrepancies that the rational value construction introduces into mathematics are as poor as the quality of your conversation here, and yet the details grow obscured by your style of conversation here. I suppose if status quo mathematics is to go on in will actually have to follow your program.

We agree that values get constructed and then operators can be applied to those values. Now all that is left is to apply this analysis to the rational value. We discover that the rational value must not be fundamental for its instances:
3/4 , 1/3 , 6/76
are in their simplest form which contains the operator. Thus no rational value exists without an operator in the value. This conflicts directly with the point of contention which you are attempting to obscure. Did you actually want to take back that detail that you now have expounded on here numerous times? As a parent teaches a child in a chess game it is OK here on usenet to take back a statement I think. Particularly if it helps the discussion go better your way. What I find particularly disturbing though is the claim that I don't believe this. From the start of the discussion the crux is exactly on this very detail that you have obscured: operators and values are distinct concepts.

[Timothy Golden]

On Tuesday, November 2, 2021 at 10:17:58 AM UTC-4, Timothy Golden wrote:
> When operators came to be embedded into numbers then mathematics lost integrity. The two terms are distinct; the value being a stable thing and the operator an action which generates another value (usually) perhaps from one value or possibly several. But of course mathematics did not evolve with these terms of distinction. Mathematics has accumulated over millennia and does attempt still to abide the accumulation regardless of detected ambiguity.
>
> The theory of types laid out be Russell is already argued as optional within his introduction to the subject. Not so of our modern compiler level languages. His types and the computer types seem to be rather different, yet is the underlying concept the same? His notation honestly was terrible; reusing symbols for ideas that are distinct is what? A typesetter's problem? Whatever; the idea of a strict and structured system has been a theme of mathematics yet the judges are human, and the accumulation is daunting. Simplicity could be had in admitting that operators and values are distinct concepts, and that when operators are embedded within the construction of numbers then such an ambiguity ought at least to go discussed rather than ignored. It is thus not only with irrational values but with rational values as well. The real number menagerie has no universal stature. As a type it is a composition of multiple types upheld as a single type with religiosity... and at this point for any to challenge the standing analysis is suicidal within the arena of mathematical drama.
>
> The falsification in short can be stated simply: A construction of a numerical representation ought not to depend on an operator that will be defined atop the construction.
>
> A concept that applies to one real value ought to apply to all real values. This theme of universality is what one ought to get religious about.
> Epsilon/Delta as universal remains to be accepted. The real number as gray is roughly where we land. This is a rather different interpretation of the continuum.

The concept or representation, as when we claim that values represent something concrete brings us straight into material correspondence. Yet we are taught that the rational value has bled into the continuum from the integer basis... thanks to that division operation which can be assessed as invalid.

So many ways to express these concepts, yet if I am correct then all defense of the rational value will not hold up. It's not as if one little mistake was made that needs correction. One big mistake was made, in hindsight, that cannot be corrected. This is an instance of a bug by design. They are the worst to remedy. The code built on an invalid assumption has little chance of coming clean.

The bidirectional nature of the digital construction: that a digit one up along the hierarchy can be studied as well as a digit one down along the hierarchy... certainly the ones place has something fundamental in it, yet the ability to shift this ones position is exactly what allows the interpretation that I am promoting. The mechanistic nature shows that no particular digit has any special position in the structure; the relative nature of the radix system is universal. Claims that the portion of the value below the decimal point are magically unique to the digits above the decimal point are refutable. Thus calling one part names such as 'fractional' can be argued as tainted. If the bottom part is fractional then so is the top part fractional as well. One need only study the tens position versus the ones position to see this fractional quality.

Particularly as we call for a representative of the continuum these details matter greatly. We accept that we are going to have to settle for a discrete representative; otherwise their will not be room to represent a single value here. That the digits below the last specified digit can be called gray or unknown is congruent with the epsilon/delta argumentation. Yes, for some systems those digits can be gotten, or chased, but as we take the continuous value seriously it must be taken quite literally that the perfection of the rational value does not exist. And to support this we would be forced to engage the material continuum: draw a line on a piece of paper and attempt to mark out say fifths, and then three of those fifths, and compare them with three more of those fifths. Obviously the perfection of the tools comes into play and the precision of the work will translate back to an actual error. No perfection will be had. One who takes the dividers and calls that unit a fifth and goes five times along the line: are they cheating? This is the most precise way to demonstrate any of the reciprocal integers cleanly. Using my argumentation above there is no problem. Coming to a large medium and working through fives of fives and so forth we will see that we are simply developing a radix five representation, yet the precision on the continuum is not actually guaranteed. The lesser cheat iteratively works his dividers until he arrives at a fifth of his earlier unit. Yet both methods will incur error.

To ask again on representing the continuum should the value itself be continuous in nature? The gray numbers are doing this.

[Serg io]

On 11/14/2021 9:09 AM, Timothy Golden wrote:
> On Tuesday, November 2, 2021 at 10:17:58 AM UTC-4, Timothy Golden wrote:
>> When operators came to be embedded into numbers then mathematics lost integrity. The two terms are distinct; the value being a stable thing and the operator an action which generates another value (usually) perhaps from one value or possibly several. But of course mathematics did not evolve with these terms of distinction. Mathematics has accumulated over millennia and does attempt still to abide the accumulation regardless of detected ambiguity.
>>
>> The theory of types laid out be Russell is already argued as optional within his introduction to the subject. Not so of our modern compiler level languages. His types and the computer types seem to be rather different, yet is the underlying concept the same? His notation honestly was terrible; reusing symbols for ideas that are distinct is what? A typesetter's problem? Whatever; the idea of a strict and structured system has been a theme of mathematics yet the judges are human, and the accumulation is daunting. Simplicity could be had in admitting that operators and values are distinct concepts, and that when operators are embedded within the construction of numbers then such an ambiguity ought at least to go discussed rather than ignored. It is thus not only with irrational values but with rational values as well. The real number menagerie has no universal stature. As a type it is a composition of multiple types upheld as a single type with religiosity... and at this point for any to challenge the standing analysis is suicidal within the arena of mathematical drama.
>>
>> The falsification in short can be stated simply: A construction of a numerical representation ought not to depend on an operator that will be defined atop the construction.
>>
>> A concept that applies to one real value ought to apply to all real values. This theme of universality is what one ought to get religious about.
>> Epsilon/Delta as universal remains to be accepted. The real number as gray is roughly where we land. This is a rather different interpretation of the continuum.
>
> The concept or representation, as when we claim that values represent something concrete brings us straight into material correspondence.

What ??

> Yet we are taught that the rational value has bled into the continuum from the integer basis...

Wrong. Analog exists first, digital is a fake representation.

> thanks to that division operation which can be assessed as invalid.

it is time for your cells to divide!

[Raleigh Hobbs]

Timothy Golden wrote:

> The concept or representation, as when we claim that values represent
> something concrete brings us straight into material correspondence. Yet
> we are taught that the rational value has bled into the continuum from
> the integer basis... thanks to that division operation which can be
> assessed as invalid.

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are fraud, and the *booster* shall be the primary you shall have!!

https://www.bitchute.com/video/0erGhgxv0LgI/
Fauci Admits Vaccines Did Not Work as Advertised and that Vaccinated Are
in Great Danger Today

[zelos...@gmail.com]

>and it is obvious to any who read along that these statements are synonymous;

False, you say APPLIED, which implies it ALREADY EXISTS.

I say CONSTRUCT/DEFINE, which implies it is made AFTER.

>This is a fine instance of you, Zelos, failing to hold a clean discussion.

I am responding to things, what you mean with "clean" is of no concern.

>This is quite a serious topic here and I pity anyone who holds the same side as you do

not really, it is just you being a crank.

>I'd like to say that you are doing a fine job holding up the status quo, but this is not quite how I see it here.

I am showing you where you are wrong, nothing else.

>Your lame defense of the status quo... really my argument deserves better than you can give. Accountability is not your cup of tea.

your arguments really deserve nothing because you do not even address the mathematics, you just attack notation like an idiot.

>The discrepancies that the rational value construction

What discrepancy? You have yet to show a single one! All you have shown is you do not understand how things are done in mahtematics and that is not an issue for mathematics!

>We agree that values get constructed and then operators can be applied to those values.

CONSTRUCTED after.

>Now all that is left is to apply this analysis to the rational value. We discover that the rational value must not be fundamental for its instances:

you're gonna be stupid again

>3/4 , 1/3 , 6/76
>are in their simplest form which contains the operator.

Yepp, you were stupid. That is NOTATION for (3,4) (1,3) and (6,76) in the construction. No operator in it.

>Thus no rational value exists without an operator in the value.

FALSE! As I have told you, rational NUMBERS are constructed as ORDERED PAIR EQUIVALENCE CLASSES.

>This conflicts directly with the point of contention which you are attempting to obscure.

Nope, because it doesn't exist as you claim.

>Did you actually want to take back that detail that you now have expounded on here numerous times?

Which? Real mathematics? Why would I take back showing you how mathematics work?

>operators and values are distinct concepts.

They are, but you conflate notation with the objects

a/b is notation for [(a,b)], it is an element

[Timothy Golden]

On Monday, November 15, 2021 at 1:02:21 AM UTC-5, zelos...@gmail.com wrote:
> >and it is obvious to any who read along that these statements are synonymous;
> False, you say APPLIED, which implies it ALREADY EXISTS.
>
> I say CONSTRUCT/DEFINE, which implies it is made AFTER.
> >This is a fine instance of you, Zelos, failing to hold a clean discussion.
> I am responding to things, what you mean with "clean" is of no concern.
> >This is quite a serious topic here and I pity anyone who holds the same side as you do
> not really, it is just you being a crank.
> >I'd like to say that you are doing a fine job holding up the status quo, but this is not quite how I see it here.
> I am showing you where you are wrong, nothing else.
> >Your lame defense of the status quo... really my argument deserves better than you can give. Accountability is not your cup of tea.
> your arguments really deserve nothing because you do not even address the mathematics, you just attack notation like an idiot.
> >The discrepancies that the rational value construction
> What discrepancy? You have yet to show a single one! All you have shown is you do not understand how things are done in mahtematics and that is not an issue for mathematics!
> >We agree that values get constructed and then operators can be applied to those values.
> CONSTRUCTED after.
> >Now all that is left is to apply this analysis to the rational value. We discover that the rational value must not be fundamental for its instances:
> you're gonna be stupid again
> >3/4 , 1/3 , 6/76
> >are in their simplest form which contains the operator.
> Yepp, you were stupid. That is NOTATION for (3,4) (1,3) and (6,76) in the construction. No operator in it.
> >Thus no rational value exists without an operator in the value.
> FALSE! As I have told you, rational NUMBERS are constructed as ORDERED PAIR EQUIVALENCE CLASSES.

How the rationals will come in as a subset of the reals is problematic under your interpretation. I do see the formal definition using the pair on nonzero integers, yet when you deny that 3/4 is a rational value then something has gone badly wrong.
I had no idea that such a tough spot existed down here in the math. Clearly the reason for your denial is exactly as I've laid it out on this thread. That the rational value 3/4 contains an operator and the evaluation of the operator yields 0.75 as a raw value is obviously true, and yet your method is going to be tortuous in order to absorb this detail. Your position is proof of the problem.

Your own need to invert my logic and awareness is the poorest of defense of the rational value. Either way it will fail as fundamental. There are simply too many ambiguities lining up against it.

Dimensional analysis tells us that a pair of values is dimensionally up one from a singular value. Until the two dimensional nature of the formal rational definition drops to one dimension via the division then this ambiguity remains.

Beyond this the complexity of the operations of the rational are all done in hindsight of the division operation. That they would care to even define division atop division places your position more in line with what you claim my position to be. This sort of miscommunication is almost bound to happen given the dirty state that you reradixers are taking.
The rational value is not elemental.

[zelos...@gmail.com]

>How the rationals will come in as a subset of the reals is problematic under your interpretation.

Not at all, there is a natural injection between Q and R so despite beign constructed differently they can naturally be said to be in subset/superset relation and Q is a subfield.

>I do see the formal definition using the pair on nonzero integers, yet when you deny that 3/4 is a rational value then something has gone badly wrong.

3/4 is a rational NUMBER, stop with the value, which is NOTATION for the EQUIVALENCE CLASS [(3,4)] in the RATIONAL NUMBER CONSTRUCTION.

>Clearly the reason for your denial is exactly as I've laid it out on this thread.

Nope, what you lay out here is nothing but your stupidity.

>That the rational value 3/4 contains an operator

False, [(3,4)] has no operator in it.

>and the evaluation of the operator yields 0.75

There is no "evaluation", 0.75 is just notation for [(75,100)]=[(3,4)]

>as a raw value is obviously true

None is "raw" here, both are different notation for the same equivalence class.

>and yet your method is going to be tortuous in order to absorb this detail. Your position is proof of the problem.

What problem? You have stated no problem. All you do is bitch about notation without understanding the construction!

>Your own need to invert my logic and awareness is the poorest of defense of the rational value. Either way it will fail as fundamental. There are simply too many ambiguities lining up against it.

Ther eis no ambiguity in the construction of rational numbers or real numbers. It is first order logicly done.

>Dimensional analysis tells us that a pair of values is dimensionally up one from a singular value.

"dimension" is only valid in vector fields and such as the cardinality for the base. When you construct real numbers and such, it is not a module or a vector field so it is nonsense and irrelevant.

>Until the two dimensional nature of the formal rational definition drops to one dimension via the division then this ambiguity remains.

There is no ambiguity here. The construction of Q as Z x Z_{>0}/~ is of dimension 1 because the basis, when made a vector field over Q itself, is {1} which has cardinality 1. But that is irrelevant to this.

https://proofwiki.org/wiki/Definition:Dimension_of_Vector_Space

as always, educate yourself.

>Beyond this the complexity of the operations of the rational are all done in hindsight of the division operation.

Division is defined AFTER the set, AFTER multiplication and AFTER the inverse!

As always, you are so fucking stupid and ignorant

[Timothy Golden]

On Tuesday, November 16, 2021 at 12:19:26 AM UTC-5, zelos...@gmail.com wrote:
> >How the rationals will come in as a subset of the reals is problematic under your interpretation.
> Not at all, there is a natural injection between Q and R so despite beign constructed differently they can naturally be said to be in subset/superset relation and Q is a subfield.
> >I do see the formal definition using the pair on nonzero integers, yet when you deny that 3/4 is a rational value then something has gone badly wrong.
> 3/4 is a rational NUMBER, stop with the value, which is NOTATION for the EQUIVALENCE CLASS [(3,4)] in the RATIONAL NUMBER CONSTRUCTION.
> >Clearly the reason for your denial is exactly as I've laid it out on this thread.
> Nope, what you lay out here is nothing but your stupidity.
> >That the rational value 3/4 contains an operator
> False, [(3,4)] has no operator in it.
> >and the evaluation of the operator yields 0.75

> There is no "evaluation", 0.75 is just notation for [(75,100)]=[(3,4)]

Consider the following values:
75 , 7.5 , 0.75
Isn't it clear that these are singular values? Certainly we can state that
75 = 75 / 1
but isn't it clear which is more fundamental? All of the values listed are base ten values. Their digits are interlocked. Whether upward toward large values or downward toward small values the mechanism by which these numbers work is the radix ten system. There is no magical separation at the decimal point. In fact, if we simply replace the decimal point with a small value indicating its position we see that the proper interpretation of the value is as a single integer which now has a secondary unit value; this secondary value being of a different type. No operator is needed within the interpretation. The integer as the sole of the value remains.

The rational value as an abstracted form '[(75,100)]' in order to dodge the operator exposes the farce of formalizing the rational value as the continuum. When in grade school we had a pie that got sliced into thirds and you could see the three slices form the whole pie. Well, the rational values did have a material basis. Yet in a continuum it is far more relevant to address the concept of the unit, and here all this math fails. The meter is no better than the foot in this regard. These 'units' are arbitrary, and here we see the great divide between the counting numbers and the continuum. The issuance of 'one' is not terribly meaningful on a material continuum. To date these issues are only resolved via bureaus of standards and that sort of gravely serious detail and overhead in the pursuit of the mathematicians' epsilon/delta levels of precision.

We do not witness a continuum of oranges, say. Instead we witness variations in the size of oranges. Geometry and dimensionality take their place as the continuum raises up beyond these simple values. Where did this lowly pair of values you insist upon disappear to? Shouldn't our (x,y) coordinates of the Cartesian plane era all be carrying these carefully placed doublets? Ahhh.... What if we found out that your doublets required sub-doublets? Then I'd have broken your theory, wouldn't I?

From operator theory we already know that you are mounting a new class of operators on top of the integer operators; that your sum requires an integer product. That your value contains division, which requires a product already, is somewhat the same problem in a more formal chain of operator theory. I'd rather strike it down in the simple form as I have already done. There is no question to me that the complications that are being introduced in the formal rational value are indicators of a falsifiable system.

What is simple is beautiful. The rational number theory lacks simplicity. The radix ten value that we use to represent large values can be used to represent small values. It is already done. What is left to be done is to allow an interpretation that carries such a simplistic turn that will convert the discrete nature of the naturals to the continuous nature of what have been called the reals. Already epsilon/delta has been inserted into the reals not for these supposedly perfect rational values, but for those little irrational gaps. It is as if the continuum got built, but not completely. In the past I've been happy to just accept the rationals as good enough, but now I can assert why I thought this... and yet in the process we wind up rejecting the rational value as it has been developed historically. But you see there is more than just the continuous/discrete awareness in this interpretation. There is more than just an awareness of epsilon/delta's universality in this interpretation. There is as well operator theory in this interpretation. I find it promising that you have already bowed to the distinction of operator and value and that you willingly abide by it within the construction of the value, since the operator would mean little without values to work upon. Without this lexical distinction there would be endless confusion in the subject. Indeed how much of the complexities of the subject are actually hits against this backboard is of interest to me. I have now discovered another, and at such a base level. The modern construction of the complex number is another fine instance, since the sqrt(-1) is not a valid constructor. The polynomial of abstract algebra has yet to admit its own needs. I suppose closure will have to be reviewed on the rationals.

[zelos...@gmail.com]

>Consider the following values:
>75 , 7.5 , 0.75
>Isn't it clear that these are singular values? Certainly we can state that
>75 = 75 / 1

They all refer to different RATIONAL NUMBERS! Stop with the "value"

>but isn't it clear which is more fundamental?

Your idea of "fundamental" is of no relevance.

>All of the values listed are base ten values.

There is no "base" for number, only NOTATION. The decimal NOTATION is base 10.

>Their digits are interlocked. Whether upward toward large values or downward toward small values the mechanism by which these numbers work is the radix ten system.

Gibberish

>There is no magical separation at the decimal point. In fact, if we simply replace the decimal point with a small value indicating its position we see that the proper interpretation of the value is as a single integer which now has a secondary unit value; this secondary value being of a different type. No operator is needed within the interpretation. The integer as the sole of the value remains.

Meaningless garbage that is based on notation. I have told you to stop arguing on notation.

>The rational value as an abstracted form '[(75,100)]' in order to dodge the operator

There is no dodging, that is how rational numbers are constructed!

>exposes the farce of formalizing the rational value as the continuum.

This exposes the complete idiocy and IGNORANCE of you!

>When in grade school we had a pie that got sliced into thirds and you could see the three slices form the whole pie. Well, the rational values did have a material basis.

Irrelevant to mathematics

>Yet in a continuum it is far more relevant to address the concept of the unit, and here all this math fails.

Nope, mathematics have a definition for unit you retard.

>The meter is no better than the foot in this regard. These 'units' are arbitrary, and here we see the great divide between the counting numbers and the continuum. The issuance of 'one' is not terribly meaningful on a material continuum. To date these issues are only resolved via bureaus of standards and that sort of gravely serious detail and overhead in the pursuit of the mathematicians' epsilon/delta levels of precision.

You are talking about two different units, physical units are irrelevant to mathematics.

>We do not witness a continuum of oranges, say. Instead we witness variations in the size of oranges.

Irrelevant to mathematics

>Geometry and dimensionality take their place as the continuum raises up beyond these simple values. Where did this lowly pair of values you insist upon disappear to?

Nowhere, we construct things but we don't write them always out like it because it is a fucking pain in the arse.

>Shouldn't our (x,y) coordinates of the Cartesian plane era all be carrying these carefully placed doublets? Ahhh.... What if we found out that your doublets required sub-doublets? Then I'd have broken your theory, wouldn't I?

Nope, because you fail to understand the difference between the object and notation.

>That your value contains division, which requires a product already, is somewhat the same problem in a more formal chain of operator theory.

There is no operator in rational NUMBERS

>What is simple is beautiful.

Agreed, the fact that we can construct all of mathematics from 9 axioms is a beautiful thing.

>The rational number theory lacks simplicity.

nope, it still stems from the those 9 axioms.

>The radix ten value

is notation, not constructoin.

>The modern construction of the complex number is another fine instance,

Not of what you want, it works just fine.

>since the sqrt(-1) is not a valid constructor.

No one defines i or complex numbers that way in mathematics.

>The polynomial of abstract algebra has yet to admit its own needs. I suppose closure will have to be reviewed on the rationals.

polynomials are closed because even there you fail to understand shit and og on NOTATION like you always do!

You never argue from THE OBJECTS, you argue from NOTATION which means ALL of your SHIT IS FALLACIOUS!

[Timothy Golden]

On Wednesday, November 17, 2021 at 12:30:34 AM UTC-5, zelos...@gmail.com wrote:
> >Consider the following values:
> >75 , 7.5 , 0.75
> >Isn't it clear that these are singular values? Certainly we can state that
> >75 = 75 / 1
> They all refer to different RATIONAL NUMBERS! Stop with the "value"
> >but isn't it clear which is more fundamental?
> Your idea of "fundamental" is of no relevance.

Of course it is. The rational is built by a pair of integers. Clearly the integer is more fundamental.
The decimal notation is readily converted to an integer by simply removing the decimal point.
What information was lost by the removal of the decimal point?
The unity position was lost.
Arguably the unity position of the integer is always at the last digit.
Obviously this form of representation does not work on a continuum.
There is a material discrepancy, yet as the unit is under scrutiny now, clearly this decimal form is quite restrictive, yet it suffices.
This is why the metric system is adopted universally.
Just how much freedom does the unit deserve?
You claim that it is well defined yet you have offered no definition.
Really all your communication is marked by insults that don't even have any clever fun in them.
I'd really rather you shafted me more craftily, sir.
Still, you do have persistence, and the thread of what remains of the denatured rational value seems to be what you are working on, and so I should attempt to bow over to that form at some level. I have just attempted that confrontation as the rational as built from the integer should hold up even under your strict version where 3/4 is not a rational value but 3,4 is. As you argue about notation of course everything that we write here is notation.
Good notation is relevant, and especially if a notational convention has been reached that hides a logical inconsistency, such as embedding an operator in a value and calling it a pure value, then that notation does deserve further scrutiny. When raw values are reached, and by this term 'raw' I mean that no operators are emebedded in the value, then some level of integrity has been achieved.

I myself have to consider this issue even on the form
s x
and to what degree is there an operator embedded there between the sign s and the magnitude x? As I generalize sign the focus has been put to the s in sx, yet now we discuss the x in sx. I had thought previously that the reals without any sign could do to describe that x. The two-signed reals are P2 of polysign. Yet this description carries around the historical baggage of reals as a union of sets Z, (Z,Z), and Qbar, I guess if you could put a label on the irrationals. This certainly is not the continuum that I think of when I want a pure value. I want a set which treats its members equally; where the epsilon/delta that applies to one applies to all. It turns out that the physical correspondence; the material connection; is completely consistent with the decimal value. When you put the perfect rational up against the epsilon/delta irrational some analysis occurs. Tradition favors the extremely different treatment that these two forms take. Modern structured thinking rejects this accommodation. Universality on the continuum dictates that every value may suffer an epsilon/delta crisis. So when your 1/3 gets evaluated to 0.333 don't go bawling to your alma mater.
Really every loser suffers a hit to their ego when their game goes bad. I do think that Zelos is suffering this badly here which would explain the level of name calling that he needs to engage in on an otherwise purely theoretical discussion.

I can sit tight and cozy with the values that my computer uses. I have changed nothing. I have offered here only an interpretation on the standing decimal number as an integer augmented with an adjustable unit position. As to who exactly is horrified by the situation: I do assure you it is another type of thought system than my own. Mathematicians are heavily engaged in mimicry. Somehow I have managed to slide out of the cell. To be completely honest with you I don't feel as though I understand half or even a tenth of standing mathematical works. In the pileup I can scarcely claim to have read a thousandth I would think of the pile. However you see one who devours such works in a way that presumes their correctness is bound to be a grand mimic. This confluence of a social animal behavior in a realm that deserves the most careful scrutiny is bound to be a tension that deserves far greater energy than academia gives to it. The well oiled machine even has oil dripping off the belts in preparation for a bearing failure. The old wrench in the gears trick won't work on this one. Obviously the sort of recourse that I envision will not be happening any time soon. Still I am free to discuss these details here and at length build my case for why these things are so.

[zelos...@gmail.com]

>Of course it is.

Nope

>The rational is built by a pair of integers. Clearly the integer is more fundamental.

ORDERED pair, If you are gonna go down that route guess what? Sets are the most fundamental in mathematics because from ZFC we can construct all of mathematics you are familiar with.

>The decimal notation is readily converted to an integer by simply removing the decimal point.

Is just notation, stop being fixated on it. I won't be responding to things that are only notation beyond saying "notation, not relevant"

>There is a material discrepancy, yet as the unit is under scrutiny now, clearly this decimal form is quite restrictive, yet it suffices.

notation, not relevant

>This is why the metric system is adopted universally.

Physics, irrelevant.

>You claim that it is well defined yet you have offered no definition.

Mathematics do not deal with such things. The unit in mathematics is defiend easily :) 1*x=x*1=x, the 1 is the unit.

>I have just attempted that confrontation as the rational as built from the integer should hold up even under your strict version where 3/4 is not a rational value but 3,4 is.

it is (3,4) moron. And rational number construction holds.

>As you argue about notation of course everything that we write here is notation.

There is a difference between USING notation and argue BASED ON NOTATION, you do the latter and that is retarded.

>Good notation is relevant, and especially if a notational convention has been reached that hides a logical inconsistency, such as embedding an operator in a value and calling it a pure value, then that notation does deserve further scrutiny.

NUMBER or ELEMENT, not value.

Here you argue based on notation again, it is invalid. 3/4 works just fine as notation and in mathematics is understood to be [(3,4)] in rational numbers.

That is why you should stop arguing it and instead understand what things mean instead of what you see.

[Timothy Golden]

On Thursday, November 18, 2021 at 12:31:05 AM UTC-5, zelos...@gmail.com wrote:
> >Of course it is.
>
> Nope
> >The rational is built by a pair of integers. Clearly the integer is more fundamental.
> ORDERED pair, If you are gonna go down that route guess what? Sets are the most fundamental in mathematics because from ZFC we can construct all of mathematics you are familiar with.

> Here you argue based on notation again, it is invalid. 3/4 works just fine as notation and in mathematics is understood to be [(3,4)] in rational numbers.
>
> That is why you should stop arguing it and instead understand what things mean instead of what you see.

Alright Z. I've had enough. Simple concessions are like pulling teeth with you. I'd rather keep covering ground than run a dull blade through the grass.
It happens that MU (minus unity) is more fundamental than NU (neutral unity), in that MU can generate NU, but not the other way around. Of course this is stated in terms of the product, and the argument I am about to make brings all of that into question. Still this fundamental ability:
(-1)(-1) = + 1 (P2; the reals)
(-1)^3 = * 1 (P3; the complex numbers with their P2 coat off)
( - 1 ) ^ a builds all signs and iterates through them as well.
could be turned onto the operators product and division. Notationally this will be a little bit challenging, but I suppose having some NUs to throw around will help the procedure. Firstly we have to admit that the product will only make the product. Yet division, the inverse operator is capable of generating the product:
a / (1 / b ) = ab

So logically is division more fundamental than the product? Does it have greater utility? Should subtraction likewise come into this fray as the more fundamental operator because addition can be expressed through it while the inverse is not true?

Here I am graying out the logic between operators and values, or at least attempting to apply a logical argument across them.
When we build or construct or develop a system we typically start with simple things firstly, then build up, and hopefully simply so, to a more advanced form that will beget some additional functionality or utility.

It seems that the logic is simple enough, yet as we attempt to declare division as fundamental we cannot help but bump into the effect that
a b = c : c / a = b , c / b = a .
That the latter two above are based on the first by definition; that the product precedes the division operator.

Possibly it suffices to simply admit that a behavior with modulo two character is arising from the derived operation division.
Regardless: we know which is more fundamental. We know that the rational numbers have embedded an operator within their construction which is not fundamental. Therefor we know that the rational numbers are not fundamental. As we seek fundamental status we have to look elsewhere, and to harken back to the integer form and to witness that every instance of a decimal value with a secondary unit point such as
123.456
may simply be regarded as a raw integer with a slight bit more of structure. The radix mechanism in use for large values does in fact apply to smaller values. There is no magical stop at the decimal point. Get over it. We still have not surpassed the integer representation. We have only augmented it.
That this augmentation is sufficient for our purposes is only answered through epsilon/delta. That epsilon/delta may now be applied to all values universally: here is a crux worth pondering.

[zelos...@gmail.com]

>Alright Z. I've had enough. Simple concessions are like pulling teeth with you.

You will get it when you deserve it and stop being stupid :)

Getting you to stop being stupid is like pulling teeth.

>I'd rather keep covering ground than run a dull blade through the grass.

Then be right for once and we can cover ground. When you are wrong I have to correct you.

>It happens that MU (minus unity) is more fundamental than NU (neutral unity), in that MU can generate NU, but not the other way around.

In your personal opinion and nothing else. Construction wise 1 is made before -1

>So logically is division more fundamental than the product?

Given we construct multiplication first and then define division in terms of it, take a fucking guess you retard.

>Does it have greater utility? Should subtraction likewise come into this fray as the more fundamental operator because addition can be expressed through it while the inverse is not true?

rings are defined in terms of addition and multiplication, take a fucking guess why.

>Here I am graying out the logic between operators and values, or at least attempting to apply a logical argument across them.

I'd like to see you try doing logic to begin with.

>When we build or construct or develop a system we typically start with simple things firstly, then build up, and hopefully simply so, to a more advanced form that will beget some additional functionality or utility.

Hence we have sets first, then build N, then Z, then Q, then R, then C

>It seems that the logic is simple enough, yet as we attempt to declare division as fundamental we cannot help but bump into the effect that
>a b = c : c / a = b , c / b = a .
>That the latter two above are based on the first by definition; that the product precedes the division operator.

only if division is definable.

>We know that the rational numbers have embedded an operator within their construction which is not fundamental.

False, when we construct rational numbers we embed no operator in them. Just an equivalence class of ordered pairs.

You are arguing from notation again.

>Therefor we know that the rational numbers are not fundamental.

False, as you argue from notation, not construction, your invalid.

>As we seek fundamental status

You seek it yet understand nothing.

[Timothy Golden]

Zelos, I won this argument when you denied that
3/4
is a valid instance of a rational value. In effect your insistence on avoiding this form is proof of my argument.

We are more in agreement than you seem to be able to admit.
Peace Be With You, Old fellow. In these Covid times I'll be sure not to miss your passing.

[zelos...@gmail.com]

You have won nothing.

I say 3/4 is NOTATION for a rational NUMBER that is PROPERLY constructed as [(3,4)]

I won't pass :) Got all my vaccines and am in good health, I do hope the reaper takes you you crank!

[Timothy Golden]

It's so sad to see you wither away on this thread. There is much to be said in the rational value's favor, but it is not in terms of any fundamental view.
Clearly a value such as
3 / 231
is quite some specification of a value whereas in the humble radix ten system we'd have:
0.012987012987
and still not be quite that figure exactly. This is where those rational values shine. I'll admit the decimal form is quite pretty too, but you've certainly done it in less digits better than I can with more than twice the digits! Of course the dirty reradixer must come along and find an even better figure. He does so as:
0.3
in radix 231. The dirty reradixer has us all beat.

[FromTheRafters]

Timothy Golden explained :

> It's so sad to see you wither away on this thread. There is much to be said
> in the rational value's favor, but it is not in terms of any fundamental
> view. Clearly a value such as 3 / 231
> is quite some specification of a value whereas in the humble radix ten system
> we'd have: 0.012987012987
> and still not be quite that figure exactly. This is where those rational
> values shine. I'll admit the decimal form is quite pretty too, but you've
> certainly done it in less digits better than I can with more than twice the
> digits! Of course the dirty reradixer must come along and find an even better
> figure. He does so as: 0.3 in radix 231. The dirty reradixer has us all
> beat.

Rational (read as fractional) values shine better in CFE than in CDE
IMO. Of course, it should be remembered that these are representations
not definitions.

[Timothy Golden]

Well then do you sir, for the moment, consider yourself to be a dirty re-radixer?

Can you beat 0.3?

[FromTheRafters]

It happens that Timothy Golden formulated :

I don't know what you mean. To me numbers are in unary representation,
no multiplicity by moving some radix point. This is representation, not
value.

> Can you beat 0.3?

I don't know what you mean.

[Timothy Golden]

Ordinarily we use a radix ten system. We simply now use a radix 231 system.
Of course that figure 231 was a radix ten value, and still is a radix 10 value.
What was 3/231 becomes 0.3 and this is quite an efficient and precise form.
The only values that are lacking in unary character here are the rational values.
They are not fundamental. I don't understand your distinction between representation and value.
I agree that there is no multiplicity by moving some radix point.
A value such as
1234
is nearly the same as
12.34
The multiplicity is clearly a digit thing; a radix quality. The little dot is not a separator. The digits are as cleanly connected between the 3 and the 4 as they are from the 2 to the 3 and the 1 to the 2. Our numeric values are words based on this elemental system. Particularly a value which is unspecified ought to be seen as quite gray in every digit; possibly like little wheels whirling around spinning through all numerical possibilities... yet all still well connected too. Clearly the blur is more blurry at the low end. Epsilon/delta shows us that there is gray to the right of the digits; roughly.
The meaning of the little dot is to where unity is in the chain of digits. You can get rid of the dot and use some other bit of information. More than a bit really, but quite a bit less than most values. Of course if you want to call it trickery then we can return to the natural value interpretation once again.

Who is playing games and who is working in fundamental numbers here?
I admit that the rational value is clever, but I deny its fundamental status.
It does not need to be entered into the continuum as a constituent and especially not as the first instance to break into the continuum.
The reasoning is most direct through operator theory.
The physical nature of the continuum preexists the rational value.
The rational value's discrete nature is merely that of the radix value.
The radix value and its usage ought not be so recessed away from the rational value.
It does great harm to mathematics to practice such an ununified mantra.
Indeed to enforce such a mantra under threat of failure is not acceptable.
Indeed the very prefix 'un' seems terrible. Have we gotten it backwards?
No, not in the modulo one form. Modulo one is unified. No radix point will do any work there. It is a return to the natural state. And yet this ultimately is what I argue for all the others too.

I am sorry to seem cryptic, buy your own language is arguably more ambiguous than mine.
There are some subtle surprises down here in the basement of math technology.

[FromTheRafters]

Timothy Golden wrote :

I see 231 as an integer value which just happens to be represented in
radix ten this time. I extend my thinking from unary discrete units to
something more befitting the reals by thinking 'how much' instead of
'how many' just as superscripts came to be known as "exponents" or "to
the power" instead of the "how many times" a function is iterated it
became how much of an certain effect is applied. We can use pi as an
exponent, and as a modulus.

> What was 3/231 becomes 0.3 and this is quite an efficient and precise
> form. The only values that are lacking in unary character here are the
> rational values. They are not fundamental. I don't understand your
> distinction between representation and value. I agree that there is no
> multiplicity by moving some radix point. A value such as
> 1234
> is nearly the same as
> 12.34

0.1111 times ten is 1.111 -- just a shift to the right for the point or
left for the significant digits. For base two it is twice, for base
three triple. For unary there is no factor like ten, two, or more
involved but also no logarithms.

[Timothy Golden]

Yes I assume here you are speaking of unary as radix one.
In other words, two is:
1 1
Is this correct?
I do think there may be some corollary down here. P1 likewise carries what would ordinarily be seen as exceptions, yet in hindsight those exceptions are simply assumptions of the P2 form. Are we possibly about to breed a P3 value in a new fundamental format? I confess I do not have it. Or I already posess it but not at this low level. In that the decimal point is free to wander in one direction only under my first augmentation it is P1ish. That operators have their inverses but no triverse is P2ish. Yet when we do witness the sum, the product, and then the power, all as relatives and in a progression then we could arguably be P3ish. Somehow it possibly lays in the fact that the sum is graphically truly the sum:
1 1 1
yet already we see the need within our nomenclature to disambiguate as to which convention we are operating by. Still, if operator theory springs a leak on the modulo one form then should there be consequences? Would all then have to flock to the radix format? Where our familiar senses lay? Should you then be forced to adopt the radix assumption?

In the simplest of terms we have
(a)(a) = a + a + a + ... a ( a times )
a + a = 2 a (ahh, a need for a two here?)
a ^ 2 = (a)(a)
a^a = (a)(a)(a)...(a) (a times)
b + a = ?
(b)(a) = b + b + b + ... b (a times)
b ^ a = (b)(b)(b)...(b) (a times)
In some regard b+a is natural or predefined or easy. The higher operations have recipes reflecting summation but are on some sort of a ramp. I typically bail out at the exponent: it never has congealed in my mind. Certainly for natural values it is easily worked. But in other ways the dirty re-radixer comes to mind. Continuous exponents have lost this simplicity laid out here, right?

In polysign the issuance of a concept like:
z^z
as a general phenomenon or computation is not granted as I understand it now. This said, I feel very muddy about this level of interpretation.
In order to install in the mind a complete instance I would ask whether in P4 I could have:
( - 1 + 2 * 3 ) ^ ( - 1 + 2 * 3 )
and if not why then can you have it in P2? The n-ary principal will possibly be fouled here.
I believe if my interpretation is correct that you are saying that logarithms do not exist in the radix one system. Do products exist? And yet changing radix these things become available? I have to own that I am a newb in this ground but it is about time that I got to it. We are in fundamental territory here, no?

[Timothy Golden]

I guess I see you are simply applying the radix formula sum of powers onto the mod-one form.
This is not so much a defeat of the logarithm. It is still consistent. I am not treating that formula as fundamental.
I am treating the digits as fundamental, as when we write down our numbers and they are considered complete and unencrypted.
To claim that all concrete values are encrypted could spell trouble to my own interpretation I suppose.
That we should not push children into a cryptic state is likewise a fine attempt.
The notion of some base level of simplicity should occur down here somewhere.
Then too we should wish of the adults in our society that they as well not be congealed into a cryptic society; One which dishes out lies for only some to read between the lines. this sort of exclusivity as practiced circa 2016 is the undoing of a short lived experiment. If for instance corruption is adopted as an axiomatic stance then one should not wonder at the results of the work. It will be corrupt.

Now clearly if we enter through this window we are approaching the system as open I think. We are engaged in a progression and are attempting here to decorrupt or disambiguate. The ambiguated system carries many levels of ambiguity; just as a corrupt axiom ought to yield.

The main reason that I can site to flee the sum of powers description of the digital value is its extreme consumption of operators. For a mere two digit value you are looking at quite a few operators and values to describe what was a singular value. Some of those operators are complicated as well. No. The radix value and its operation as an incremental system are clean and proven without the ambiguity of the sum of powers. Yet is there a class of operators buried there? When we increment the value
1.23
to
1.24
and eventually
1.29
to
1.30
has an exception occurred? Carry? Reset? Or is it just another incremental step along the way? The digits do interact. These interactions are special. But they are regular and well defined. They are as regular as the base is. Maybe this is how the binary form rules our computers: the exceptional form is just as prevalent as the nonexceptional form. Somehow the human mind has settled into that binary assumption on sign. It is the worst mistake that humans have made. Barely even have they adopted sign so it seems to me now that I have attempted to dip back a little ways. The misnomers in the language are substantial. But here we discuss something other than sign, and I am sorry to confuse the content with this sidetrack. Here we are down to raw values in the radix form. Of course somewhere along the way we should return to the rational mindset.
I wonder Rafters, is
3/4
a rational value? Are you going to have to tip-toe around this? Would you care to flog Zelos for me?

[FromTheRafters]

Timothy Golden has brought this to us :

That, yes, but the important consideration, that is the 'take away'
was, that same base representations (base ten for instance) with
exponents the exponents can be added with the result being the same as
if the two base numbers had been multiplied. An essentailly preserved
attribute similar to the way addition and multiplication play well
together for the distributive property to work.

Things get a little less intuitive, but there is method to our madness.

[FromTheRafters]

Timothy Golden was thinking very hard :

> On Saturday, November 20, 2021 at 9:06:46 AM UTC-5, Timothy Golden wro

[...]

> I guess I see you are simply applying the radix formula sum of powers onto
> the mod-one form. This is not so much a defeat of the logarithm. It is still
> consistent.

Here I use the "pipe" character as a tally-mark. Using a 1 might make
people think it is a one.

Two plus two equals four ||+||=|||| Concatenation (+) represents
addition and repeated addition can be seen as

Two times two equals four (||)*(||) = |||| Because the one tally value
tells us the other tally value is to be added to itself that many
'times'. In an additive group, this would be an exponent. This
notation, it gets messy. If we use two glyphs, we can 'write' the
numbers more efficiently - twice as efficient. Now we have a length to
associate with the 'writing' of a number. Still a little messy, but in
base ten you can more clearly see how written length relates to
logarithms. Multiply ten by ten, and it gets one digit longer.
Squareroot any number less than one hundred and you get a one digit
number in base ten. Such relations don't exist in unary
representations, logarithm is not defined.

> I wonder Rafters, is 3/4 a rational value?

It is a representation of an element of Q -- the rational numbers. From
the same equivalence class as 75/100 which means we can also represent
it as 0.74999... from Q as embedded in the reals.

> Are you going to have to tip-toe around this? Would you care to flog Zelos
> for me?

For me, a number's value is what lies behind its representation. I have
a value in mind but to convey it to others I have to represent it in a
fashion in which they are familiar. For me, numbers, as values, have an
existence of their own even when we are not talking about them.

[Timothy Golden]

On Saturday, November 20, 2021 at 11:57:05 AM UTC-5, FromTheRafters wrote:
> Timothy Golden was thinking very hard :
> > On Saturday, November 20, 2021 at 9:06:46 AM UTC-5, Timothy Golden wro
> [...]
> > I guess I see you are simply applying the radix formula sum of powers onto
> > the mod-one form. This is not so much a defeat of the logarithm. It is still
> > consistent.
> Here I use the "pipe" character as a tally-mark. Using a 1 might make
> people think it is a one.
>
> Two plus two equals four ||+||=|||| Concatenation (+) represents
> addition and repeated addition can be seen as
>
> Two times two equals four (||)*(||) = |||| Because the one tally value
> tells us the other tally value is to be added to itself that many
> 'times'. In an additive group, this would be an exponent. This
> notation, it gets messy. If we use two glyphs, we can 'write' the
> numbers more efficiently - twice as efficient. Now we have a length to
> associate with the 'writing' of a number. Still a little messy, but in
> base ten you can more clearly see how written length relates to
> logarithms. Multiply ten by ten, and it gets one digit longer.
> Squareroot any number less than one hundred and you get a one digit
> number in base ten. Such relations don't exist in unary
> representations, logarithm is not defined.

OK, yet it is true that
1111 = 1 x 1 ^ 1111 + 1 x 1 ^ 111 + 1 x 1 ^ 11 + 1 x 1 ^ 1
That was supposed to end in a zero but we don't have any.
Why? That zero was a side effect of the modulo counting.
Somehow we are off by one... again.
Indeed the first naturally occurring zero is in radix two.
Ambiguity, anyone?

> > I wonder Rafters, is 3/4 a rational value?
> It is a representation of an element of Q -- the rational numbers. From
> the same equivalence class as 75/100 which means we can also represent
> it as 0.74999... from Q as embedded in the reals.

So I am going to take this as a 'yes, Tim, 3/4 is a rational value.'
In all your padding you've managed to dodge your comfort level with including operators in your values.

> > Are you going to have to tip-toe around this? Would you care to flog Zelos
> > for me?
> For me, a number's value is what lies behind its representation. I have
> a value in mind but to convey it to others I have to represent it in a
> fashion in which they are familiar. For me, numbers, as values, have an
> existence of their own even when we are not talking about them.

I do accept your description here as authentic, and I am close by to some of it. Still I think it is a bit naive. For the love of numbers I see your position as good but no doubt your own usual position is to escape away from the digits as rapidly as possible. Instead, if we keep our noses into them a bit longer we'll possibly break into some new ground.

As you keep mentioning logarithms, I am caught reverse interpreting to exponents. These are inverse operators and the primitive I believe is the exponent as has already been exposed in a chain of sum, product, and then exponent. As to when exponents take on trickiness... we are seeing trickiness quite a bit farther back in the chain now with the very basis of the real value coming under scrutiny. The one thing I do believe will stand at the end is the radix form. Now some will take a chain of digits like:
abcd (base r)
as:
a r^3 + b r^2 + c r ^ 1 + d r ^ 0
and there is the zero I spoke of earlier, in case you missed the error that did not break anything. Possibly for the sake of bringing the radix one digit into normality we could claim that our exponent notation is off by one. After all that little caret that I've just thrown in may not be so trivial, especially at the level we are working. Why should it break at radix one? It should not. In fact this may be another falsification of the status quo mathematics. Ahh, but did it break at radix one? At the very least we have identified an ambiguity, whether consequential or not. The fact that we are onto zero and its existence is a pretty fair concern.

There is another route however that brings this interpretation of the digits under scrutiny, for we are now describing large numbers with large numbers. The idea that the exponential expansion of the digital form sheds any light on the meaning of the digit chain is fraudulent. Let's consider the two digit value:
10 (base ten; 1234567890)
Here lays the first large digit, so let's now see what that exponential expansion does for us:
10 = 1 x 10 ^ 1 + 0 x 10 ^ 0
and we see that on the lhs we have one usage of 10 and on the rhs we have two. Is the rhs any more fundamental? Now let's go on to a truely large value and see whether the exponential form sheds any light on things:
998877667554433221100
That's quite a large value. It has 20 digits in it. The first nine is going to contribute:
9 x 10 ^ 19
to the overall value. Brilliant. What does this mean? This formula can only be regarded as a translator of one radix to another radix. It sheds no light on the native radix values, and this is why the trivial math that we are familiar with here holds. Worst of all though, we are describing a large value with large values, and in this regard this method of dissection of the number is meaningless.

As we attempt to dissect our math system by awareness of operator versus value clearly the exponential 'interpretation' of a digital value is a loser.
Is all of that math really going on under the hood of the humble radix value? How did our children learn it so easily then? Long before they had any idea of these bigger concepts. Indeed it seems that we learned the exponential form more from the digits than the other way around. The conversation on math takes interesting turns down here. We have grammar clearly already on the stake and would like to cleave our values from our operators cleanly wouldn't we? Then into the fold comes symbolism, powers, and all sorts of political; nay religious; doctrine. Mathematician turned grammarian? Where was Chomsky when all this unfolded? Oh, he was telling us to vote for Hillary Clinton, along with Amy Goodman and Juan Gonzalez... what a bunch of winners. Russiagate has sealed their fate, and none will act the wiser. Here too on usenet where perfection is optional we see roughly the same sort of dodge, even from the best here. Truth is freedom, and when a liar is exposed, well, double down sir.

[zelos...@gmail.com]

>Profilfoto för timba...@gmail.com

>It's so sad to see you wither away on this thread.

How? I am showing you wrong :)

>There is much to be said in the rational value's favor, but it is not in terms of any fundamental view.

And here you go on about your irrelevant shite.

>Clearly a value such as

NUMBER

>3 / 231
>is quite some specification of a value whereas in the humble radix ten system we'd have:
>0.012987012987

Those are not the same

>and still not be quite that figure exactly. This is where those rational values shine. I'll admit the decimal form is quite pretty too, but you've certainly done it in less digits better than I can with more than twice the digits! Of course the dirty reradixer must come along and find an even better figure. He does so as:
>0.3
>in radix 231. The dirty reradixer has us all beat.

All you're arguing about here is just notation, who cares?

[Timothy Golden]

On Monday, November 22, 2021 at 12:22:12 AM UTC-5, zelos...@gmail.com wrote:
> >Profilfoto för timba...@gmail.com
> >It's so sad to see you wither away on this thread.
> How? I am showing you wrong :)
> >There is much to be said in the rational value's favor, but it is not in terms of any fundamental view.
> And here you go on about your irrelevant shite.
> >Clearly a value such as
> NUMBER
> >3 / 231
> >is quite some specification of a value whereas in the humble radix ten system we'd have:
> >0.012987012987
> Those are not the same

sage: a=3;b = 231;numerical_approx( (a / b ), 100)
0.012987012987012987012987012987

Any better, Z? It seems sage is undergoing some troubling changes. That's only thirty digits.
You should see how bad the colors are too.

> >and still not be quite that figure exactly. This is where those rational values shine. I'll admit the decimal form is quite pretty too, but you've certainly done it in less digits better than I can with more than twice the digits! Of course the dirty reradixer must come along and find an even better figure. He does so as:
> >0.3
> >in radix 231. The dirty reradixer has us all beat.
> All you're arguing about here is just notation, who cares?

Not at all, Z. The interpretation of the glory of the rational value is in its ability to consider halves, thirds, fourths, fifths, and so on. It is the case that the rational value is merely a reinterpretation of the radix value. You sir are a dirty re-radixer, though you don't see it yet. I'm afraid that even if you did see it your own integrity is of such a poor grade that we'll be serving you that ball all day long and get nowhere on the return; roughly where you've landed here. Denial is one stage of development... unless you get stuck there. Now let's see if I can put it under your nose a little bit further.

As we discuss a value such as
3 / 231
which incidentally Rafters says is a rational value, whereas you insist that this is not a rational value. I do accept that it is a rational value, and I have no idea how you could land on such poor ground. Regardless of the subterfuge that the status quo is bound to proliferate against this humble instance, I do believe all will agree that the lower figure in that arrangement of two values and an operator; that '231' is expressed already in a radix ten system, and to disambiguate here I must state that that figure is from the codex 1234567890. There. Now we have fully described it. So you see there is a hidden value in that value. Of course the pure form occurs when we transition to a radix '231' system. After all we are discussing 231'sts of things right? Please note that I do not have a codex for '231' nor do I wish to garble things here by going to modulo one. So I have to confess that the language I am using here does carry ambiguities that nobody has resolved yet. In effect the rational number is a mixed radix system. To ignore this detail within rational analysis makes a blasphemy of all mathematics that rests on this shore. It is thus that the dirty re-radixer is born. You, sir, are a dirty re-radixer.

This is not the complete analysis though. We see that the original value, upon absorbing the radix analysis boils down to:
0.3
and here again I must confess that were the original value say 23/231 I would not have such a straightforward answer as the codex is not ready. In some regards this forms a halting problem but for the saving grace of the modulo one system, and yet the obnoxious nature of the beast as
11111111111111111111111 / 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
is not going to help matters... but then oughtn't I to have simply chosen simpler values? No! At least it is fitting on three lines of my screen here now and so it is workable. I would say if this grew to three pages I'd rather not use this notation. And yet in the terms of obnoxious values the same problem can be arrived at even in a base 10 system. Indeed stringers have gotten into obnoxious usage of scientific notation as well. The point of pushing into these places is not a draw for me. The six as an early zero is distinctly side-trackish yet the fit here in terms of realizing that these simplistic stages of number theory; the idea that before the mathematician there was a tool in the other hand ready to do some material work... all of these details fit in here at this fundamental level. The arabic numerals themselves are a form of accumulation. We face a subject which has accumulated into the current state. As such, and as any language goes, ambiguities have been absorbed if only so that the same language could be used across cultures. Indeed, if logic ever were strict it is now in this age of electronic hardware whose software has now yielded how many languages? In how much time? To infer that the human has some problems in this department is not far from the marks here. Yes, though this is not proven it is supported here in this rational analysis and the details that go overlooked in the math departments around the world in order that they yield consistency. That form of consistency is mimicry. I must warn you of the power of that force. But of course the performers who arose generation after generation are great mimics. Then too there are variations. The ones who took variations atop the absorption of the works; these are the ones who are the true greats. They found new ground. What are we doing here, but seeking new ground?

In short, should you come to the realization that the digits
a b . c d
are no differently connected from the a to the b as the b to the c and the c to the d, then you will see that the little dot in the middle is an artifice added atop a natural value. Indeed it shows us that the unit value is the third digit. It marks a secondary unity. Well possibly we will arrive one day with a tertiary unity, and of course to go to an n-ary form will make perfect sense, and general dimension will be born from a singular number. These are discrete geometries. They wind and scan and carry inherent order; not arbitrary order. Of course it will be nice to insert some commas. Here is a construction of the ordered series as a singular value. Informational analysis on this form will likely be productive, yet the confusion that could occur with it ought not be encouraged. Arguably avoidance of the Cartesian product has been achieved here.

Somehow my mind is bridging from counting to some imperative on counting of types. Sadly those types which lack discrete character seem to conform to the continuum, at which point their countability comes into question. Yes, we can operate on an artifice, yet if the material fails to conform what then? Clearly the continuum wins fundamental status over the discrete. When the two come into alignment and we can translate, even imperfectly, then we have arrived. This is the status between the radix systems, and these are discrete compartments. Yet the connection to the continuum and its availability in the native form is so easily demonstrated that the traditional interpretation shows itself as weak.

[FromTheRafters]

Timothy Golden wrote :

What I actually said was that it represents an element of Q. Your other
attempts at using other representations fell short due to your not
indicating that the repetition continues. All were different values,
yet all were in Q since they terminated or repeated in CDE
representation.

[Kip Foh]

FromTheRafters wrote:

> What I actually said was that it represents an element of Q. Your other
> attempts at using other representations fell short due to your not

of course not, Kamala Harris Was the 1st *woman_PRESIDENT* For Two Hours
While Biden Got His Colonoscopy.

[Timothy Golden]

I'm sorry I don't see the distinction.
Anyway, there is no repetition in
3 / 231
nor in
0.3
so I'm guessing you just don't like the radix translation? Or is it that you don't accept
1 / 231
as a decimal value?
sage: a=1;b = 231;numerical_approx( (a / b ), 100)
0.0043290043290043290043290043290
You want some dots on the end?
As far as I can tell Rafters, you are not saying that
3 / 231
is not a rational value are you? I'm not quite sure why this is so difficult.
I guess I must be onto something if you have to tip-toe around like this.
To be polite I suppose I could try to restate as:
" 3 / 231 is in Q"
yet this is a more cryptic statement. Q is the rational numbers, right?
What a number versus a value? These are synonymous as far as I can tell.
I don't mean any trickery here. If anyone is being tricky it is you.

"Our analysis favors, once more, a scenario below the black disk, providing an asymptotic ratio consistent with the rational value 1/3,"
- http://search.arxiv.org:8081/?in=&query=%22rational%20value%22

[FromTheRafters]

Timothy Golden formulated on Monday :

No, but 0.(004329) would at least point out its infinitely repeating
nature.

> As far as I can tell Rafters, you are not saying that
> 3 / 231
> is not a rational value are you?

No, but you haven't convinced me that it is not simply a symbol for an
element of Q rather than a three or five symbol string with operators
mixing with symbols for values like for instance the familiar numerals.

Is 231 not really something ultimately composed of hidden operators?

When I see the slant character I think of a/b as a ratio which may or
may not be determined later to have been in Q or R. If a and b are in Z
then the result is in Q.

> I'm not quite sure why this is so difficult.

Maybe you're just tired. :)

> I guess I must be onto something if you have to tip-toe around like this.
> To be polite I suppose I could try to restate as:
> " 3 / 231 is in Q"
> yet this is a more cryptic statement. Q is the rational numbers, right?
> What a number versus a value? These are synonymous as far as I can tell.
> I don't mean any trickery here. If anyone is being tricky it is you.

It's not that tricky. Division is defined in the integers. It is a
partial function, it works for a subset of integers but some resulting
values fall outside the set. We extend our set to include the
'outliers' and redefine division as inverse multiplication of ordered
pairs of integers.

[zelos...@gmail.com]

>Not at all, Z.

Yes, all you ever do is argue from notation.

>You sir are a dirty re-radixer, though you don't see it yet. I'm afraid that even if you did see it your own integrity is of such a poor grade that we'll be serving you that ball all day long and get nowhere on the return; roughly where you've landed here.

Comes from the one that only argues about notation and never the actual objects.

>As we discuss a value such as
>3 / 231
>which incidentally Rafters says is a rational value, whereas you insist that this is not a rational value.

rational NUMBER is what I say that we construct as [(3,231)]

>I do believe all will agree that the lower figure in that arrangement of two values and an operator;

Where in [(3,231)] is there an operator?

None what so ever. This proves that you argue from notation, not the object.

>that '231' is expressed already in a radix ten system

base 10 is standard notation for humans, so fucking what?

>In effect the rational number is a mixed radix system.

Nope, rational numbers is of no radix because it is a number system independent of notation. We use however base 10 when we write it on the paper for ourselves.

>It is thus that the dirty re-radixer is born. You, sir, are a dirty re-radixer.

I got no clue what that is, all I know is that you argue from notation and radix is nothing BUT notation and notation is not relevant in mathematics other than convenience.

T

[Timothy Golden]

I never thought I'd see this low level from you , Rafters. You are now approaching the level of integrity of Zelos.
There has never been any confusion of going back to integer division. Always my concern is on the rational value which enters into the reals as the first values of interest on what we know as the continuum. Prior to this formal type there were just the integers. What a shitty debate. Thank you very little.

I believe once again that I have won this debate reflecting on the difficulty of this responder and his own inability to discuss
2 / 3
as a rational value. At last he has uttered the word 'operator' but of course as a shield that will not work. The only way I've gotten him to confess this level is by quoting external sources that use exactly the same language that I use. I am not invoking any trickery in my analysis. I merely stress the distinction between values and operators. In hindsight the rational value will not make it out of its own box; certainly not as a fundamental value.

I can just see the joy in the mathematicians' eyes as they takes a measurement on his rational ruler and one says:
' That's two and 13 sixteenths.'
and another says:
' No, that's twelve fifteenths, certainly.'
to which the prior says:
'Well, I suppose if you want to get more precise we'll have to get to twentieths won't we?'
and the other says:
'Hmmm... thirtieths, perhaps...'
and the first says,
'Oh, hang on, thirty seconds are there as halves of sixteenths!'
and the other says,
'Bravo chap, you've saved us so much work!'

[Timothy Golden]

On Monday, November 22, 2021 at 11:58:00 PM UTC-5, zelos...@gmail.com wrote:
> None what so ever. This proves that you argue from notation, not the object.
> >that '231' is expressed already in a radix ten system
> base 10 is standard notation for humans, so fucking what?
> >In effect the rational number is a mixed radix system.
> Nope, rational numbers is of no radix because it is a number system independent of notation. We use however base 10 when we write it on the paper for ourselves.
> >It is thus that the dirty re-radixer is born. You, sir, are a dirty re-radixer.
> I got no clue what that is, all I know is that you argue from notation and radix is nothing BUT notation and notation is not relevant in mathematics other than convenience.
>
> T

No Z. Certainly the radix notation precedes the rational value.

[FromTheRafters]

Timothy Golden presented the following explanation :

You say that like it's a 'bad thing'. :)

You want something elemental, but you won't accept elements as that
thing, instead you obsess about nomenclature as if the labels are the
things.

--
|
This is not a pipe

[Timothy Golden]

I would think that any careful reader will see the subterfuge that two status quo positions have now taken.
One is Zelos, and the other is Rafters.
Neither will admit
1/3
as a rational value. As to how this has occurred: it is completely due to my own extreme plodding on the awareness of the embedding of operators into values as an offense to structured thought; a subject that you will see neither of them come to the table on. Actually, Zelos did manage to come to the table on this and so I have to regard his own effort as more than Rafters. Sadly though when Zelos did approach he did so fraudulently, and his argument is cause of his own dismissal of the value above as a fundamental value. Now Rafters is on the rope for the same trouble and he doesn't know which way to turn. A discrete answer has not been forthcoming. As we concern ourselves over the construction of number systems the admittance of the rational value into the reals is a position so readily accommodated by the masses, and yet this operator dysfunction accrues into the reals as a result. The notion that the reals are some pure continuum so carefully and thoroughly built as to introduce three divergent types of number within itself (the integers, the rationals, and then finally the irrationals) and treat these numbers not as one set but as three: here lays a quagmire that the moderner ought to disambiguate. This seems not to be the mathematicians place. I see that epsilon/delta can apply to all of the above. I see that material correspondence does matter. Indeed in matters of the continuous versus the discrete and which breathes life into the other it is possible that a complete inversion will occur. Every digit is capable of being extended in either direction. This is a natural scalar effect of the radix system. In that the radix system comes first, and that there is a strong and critical overlap with the rational value system, then it is the rational value which deserves the scrutiny, and this is without even invoking the operator conundrum.

[Timothy Golden]

On Saturday, November 20, 2021 at 11:57:05 AM UTC-5, FromTheRafters wrote:

> . Timothy P. Golden was thinking very hard :
> > On Saturday, November 20, 2021 at 9:06:46 AM UTC-5, Timothy Golden wrote something like:
> ["If this format was worth a dam it would already know what to do with this..."]

> > I guess I see you are simply applying the radix formula sum of powers onto
> > the mod-one form. This is not so much a defeat of the logarithm. It is still
> > consistent.
> Here I use the "pipe" character as a tally-mark. Using a 1 might make
> people think it is a one.
>
> Two plus two equals four ||+||=|||| Concatenation (+) represents
> addition and repeated addition can be seen as
>
> Two times two equals four (||)*(||) = |||| Because the one tally value
> tells us the other tally value is to be added to itself that many
> 'times'. In an additive group, this would be an exponent. This
> notation, it gets messy. If we use two glyphs, we can 'write' the
> numbers more efficiently - twice as efficient. Now we have a length to
> associate with the 'writing' of a number. Still a little messy, but in
> base ten you can more clearly see how written length relates to
> logarithms. Multiply ten by ten, and it gets one digit longer.
> Squareroot any number less than one hundred and you get a one digit
> number in base ten. Such relations don't exist in unary
> representations, logarithm is not defined.
> > I wonder Rafters, is 3/4 a rational value?

Here I believe I have been forced to foist this simple question upon the status quo and I seem not to be able to get a clean answer back.
Zelos has already given a clear 'no'.
Now, poor squeaky Rafters, hemlock may he be, and I mean that in a good way, for those who know hemlock Rafters know him to have a decent amount of integrity. Prior to this interaction I would have granted more. Instead this was his response:

. > It is a representation of an element of Q -- the rational numbers. From

. > the same equivalence class as 75/100 which means we can also represent

. > it as 0.74999... from Q as embedded in the reals.

. > > Are you going to have to tip-toe around this? Would you care to flog Zelos

. > > for me?

. > For me, a number's value is what lies behind its representation. I have

. > a value in mind but to convey it to others I have to represent it in a

. > fashion in which they are familiar. For me, numbers, as values, have an

. > existence of their own even when we are not talking about them.

[mitchr...@gmail.com]

Operations need absolute values...
zero math is a subtraction operation limit.

Mitchell Raemsch

[Timothy Golden]

And as if everybody who jumped on board with HRC can claim innocence here in the court of the public vote: dear hangers on, it is for me to tell you that something very bad has happened. That this thing is large and larger than the few election cycles which built it out. Electioneering politics? Sure it deserves its own term. Its own law... and lawyers, and accountability, and all that. We have only just begun a major sweep not just of an old generation but of their way of life too; please, yes. Yes, Please. End them and their politics now. As the end of the Republican party is proven by DJT; under Obama's watch; Boehner at the helm smoking cigars with Obama. Biden the next commensurate insider plays the center and pleads forgiveness how exactly? Lock Her Up?