Is 333...34 a valid number?

[Timothy Golden]

Is 0.333... a valid number?
If so then by the structural argument the title's answer is yes.
The decimal place is obviously a structural augmentation to the natural value.
A long string of digits is all that is left to digest.
Well there is slightly more. Are numbers two-sided?
Isn't this cause to reject the usual decimal representation of 1/3 and insist instead upon:
1/3 = 0.333...3
to secure the rhs? Now we have the initially built natural value though it is in an infinite form.

To argue that the value of the digits are infinitessimal in the 1/3 instance does nothing to the informational representation. Likewise epsilon/delta will suffice just as it does for the irrational values as Dedekind presented it. The fact that the digits are redundant is handy. Still better if we went to modulo three representation one third would simply be 0.1 and so no puzzle even ensues.

For those who like infinity I would think they'd like to let in this infinite value representation of a natural value.

For those of us who do not like this form we should then reject it as well back on the accepted repeating decimal result of the 1/3 computation. The augmentation of the radix point to the natural value exposes a special representation that is not taken seriously by mathematics so long as it is regarded as the rational value all over again. It is not. The division operation has been removed. A new unit value has been achieved.

As we approach this play on unity with fresh eyes we could even push it farther so that a new unit position of say 123 is enforced. Of course what we will have is the concept of the rational value, except no division is necessary. Now we have a counting form of the rational value. This is apt I think. Addition is far more fundamental than division. Also though this concept of unity as bridging to the concept of unification through unitization raises the lid on an otherwise closed down and done thought process. At the bottom of it all is the modulo number. the 123 as a unit instance is nearby to a reradix, sir.

These issues of course bleed onto the continuum and what we mean by it. What we even mean by countable can be broken down but for the mathematician's pure form of it in the natural value. Here now I come to wonder if even that form is undeserving of its name. Rather than 'natural' these ought to have been called 'perfect' or some such, 'exact' perhaps. 'Discrete' is pretty good though a bit more generic. Nature is far more tricky than the natural number. Reality versus the real number; well; you'll need three of them at least. Is each one then a third of reality? I do mean to belittle the terminology because deference to the past assumptions is likely partially to blame for the bottleneck that we are facing. As you bow to the masters who came before in a long chain of masters who bow to their masters your own mastery is suspect I believe. To cover the ground in a new way could be instructive particularly if we arrive at some new options.

Under the structured approach, as we legitimate the radix point as a data structure, sign comes next. There I already have productive results. Here I cannot say yet. There is movement at least in terms of interpretation, and the fact that interpreting the unit could hold this far is encouraging. The rational value as broken has been established already. That I've come around to a new form of it through the unit interpretation feels pretty good. Best of all we are back to incremental counting and modulo principles. Exactly how polysign took off. Exactly how digits work. Spacetime is structured. Whose job it is to get it from thin air: will physics ensue directly? Should our concept of number get us here? Wouldn't this actually be the real number? Has mathematics taken itself hostage through its nomenclature? What an accumulation has occurred, and for those who manage to map it all like the lines of a bible; well; have they really done themselves any favors? When does simplicity cut in? Where does complicity leave you? I so must insist that I am not complicit with the actions of my government. To see through the eyes of a juror who bought Russiagate and in the midst of near nuclear war should a few mistakes happen... Sussman is off by propaganda alone. Triple down...

[Ross A. Finlayson]

You might look to Simon Stevin, and the p-adic numbers.

The ....3334 isn't so much the "beginning" of a number as
"terminus", or interminus, you know in decimal that 3 repeating
is 1/3 so it looks most exactly a consideration that "according
to carry in arithmetic, 10 - 3 - 3 = 4, that 1 - 1/3 - 1/3 according
to carry in arithmetic, wouldn't not end in 4".

In fixed point and floating point there is, "rounding mode",
the MACHINE INTEGERS here are scalars and often basically
native to the arithmetic, floating point, or scalar units, ...,
vis-a-vis usual coordinates combined, transformed.

The units, and, the modular, with geometry's tools handy,
are very regular for usual matters of scale and precision.

Keep in mind that fundamentally the relation is continuous,
numbers in infinite representation, MACHINE INTEGERs are
fundamentally discrete, or digital, with respect to the
representation of numbers that according to register format,
have defined representations in fixed-width scalars (binary).

[sergi o]

On 6/1/2022 9:47 AM, Timothy Golden wrote:
> Is 0.333... a valid number?
> If so then by the structural argument the title's answer is yes.

If not, then by the structural argument the title's answer is no.

> The decimal place is obviously a structural augmentation to the natural value.

but its natural value is 0.333...

> A long string of digits is all that is left to digest.

0.333... is not a meal.

So I see you have a question on Math nomenclature.

> Well there is slightly more. Are numbers two-sided?
> Isn't this cause to reject the usual decimal representation of 1/3 and insist instead upon:
> 1/3 = 0.333...3

that is written wrong. corrected: 1/3 = 0.333... or 1/3 = 0.33(3)...

> to secure the rhs? Now we have the initially built natural value though it is in an infinite form.
>
> To argue that the value of the digits are infinitessimal in the 1/3 instance does nothing to the informational representation. Likewise epsilon/delta will suffice just as it does for the irrational values as Dedekind presented it. The fact that the digits are redundant is handy. Still better if we went to modulo three representation one third would simply be 0.1 and so no puzzle even ensues.

is mod3 of 0.333 base 10 = 0.1 (base3) or 0.1(base10) ? better check...

[Timothy Golden]

Alright, I will swaying slightly towards your MACHINE INTEGER awareness, in that numbers are machines. There is a bit of built in mechanics into them. Any time we instantiate a number we have somewhat relied upon the machinery to get us that value. To what degree then in the naturals if I mention 123 must you implement an increment to establish this value is somewhat required by the rules of the successor. We have short-cut that method with our digits, along with the fact that this value came out of thin air and is totally arbitrary. This sounds a lot like the description of n, except that we have fixed the digits here and no further motion should occur. The value should not go running off like WM does. If you don't like this approach, then perhaps your natural numbers cannot take any instantiated form.
The fact remains that upon instantiation, and I do believe that 123 is a fully fixed value; then the mechanism has halted and that numerical mechanism works no more. At this point the operator versus the value takes more meaning than under the variable form, whereby a value may still have some action. I do sense openings here in the classes of what are known as values, constants, and variables. That these possibly deserve some stricter treatment may expose that there are more categories than are appreciated by the mathematician. Along with this comes the abuse of forms, and no doubt there are plenty of those. If for instance one man looks at the value 123 as containing 122, 121, and so forth all the way back to naught, whereas another man is looking at that value as a freestanding singleton amongst peers yet one who knows his order, well, these distinctions could have consequences.

The notion that some fixed value could actually matter is somewhat gone from the intellectual view of the natural number. Yet if ever there were such a thing as 123 mattering: would it be a new interpretation of unit? Is this a unital claim? Pretty clearly now as we trot our way up to it we will have some sense that we are getting quite close as the counter rounds 119 and flicks up to 120. As we get past this magic value what then? Would we have some sense of the variables distance beyond 123? Of course this would be the case. In this way the very notion of a fixed value as one which matters has engaged modulo thinking. Obviously the rational value is right nearby to this. Yet this is not the rational value. This is a stage more primitive than the rational value. Do not attempt to encompass a simpler thought by a more complicated paradigm, for if you do then you have offended structural thinking. Struct and strict are nearabout to the same thing, sir. Let your inner compiler churn, please.

In some ways men of and by the natural value refuse to bow to the radix. The poor one who instantiates a value such as 123 is surely lost. Especially if he failed to mention the radix of his value then he is especially lost. If he stated that he is working with radix 10 then he is particularly and especially lost in an oblivion of such systems. In this regard, and I do accept this is a momentary but new interpretation, the issuance of a constant is inherently a two dimensioned thing, for a value without its radix is an incomplete form of number. That we are free to strike out with a declaration that all values be under one radix; then we could set forth in a course of work that would seem unambiguous. Yet to the passerby when we implemented the new radix in terms of the old radix then a compiler error was born. This exceptional state is commensurate with the secondary unity statement or interpretation. This term 'exception' is consistent with that which does in fact go on in hardware and can become a rather messy thing. So there we have it. Those sensitive enough will see the connection.

This interpretation quickly leads to something like the rational value. Yet structured thinking exposes that a careful awareness of and on unity is underway. You could call this an inversion, but what lays next is biversion and triversive thinking. Already humans are stifled in their biversive state:
Inverse( Inverse( a )) = a.
They don't seem able to ponder:
Inverse( Inverse( Inverse( z ))) = z
but this is a mangled form. It is merely put so as to shake one up and out of the prior form. The frontier of sign has been born, yet unvisited by so many as I put down the welcome mat; lay a stone arch and garden walls.

I shouldn't even join it in here. It is still a misfit. The universe maybe needs to be fit into the progression. Is to utter that word to collapse all to a single point? It is a single point of reference; the term 'universe' and in this way this interpretation may be quite good. Thence as we concern ourselves with the expanded forms we are not so much concerning ourselves with the universe as with one portion of it; one expansion of it. Strange that a logical thought could yield such correspondence.

[Ross A. Finlayson]

Yeah, when it comes to MACHINE INTEGERs, which are digital and finite
and also unbounded in a usual sense of state and access a machine,
then mostly I am reminding myself "the universe is infinite" and
"time is universal", that the INTEGERs themselves, are not necessarily
"machine" integers, that MAN is not MACHINE.

I.e. I long ago gave up any hope of a "digital universe" or "finite universe".

Of course any model of machine arithmetic is one, ..., just not "the" one.

I think you are happiest with the Brouwerian notion of the continuum,
that there's the detail _inside_ the number, while an often enough notion
of the continuum the geometric is of course fully included. So, as much as
for the spaces of geometry and what are numbers, there is digital encoding
for example in the numbers, also "continuous coding".

It's fine to exchange the lattice under state, or values, and flows for example,
or "numbers", that result evolving in time of course dynamics: it is representations
that express the values, ..., regular ways to frame your numbers.

Of course when I say lattice I just mean the infinite INTEGER lattice, that
establishes a most usual grid as a space, ..., and the infinite REAL lattice,
which it supports.


The infinite-valued and infinite-dimensional, ..., lattice.

[zelos...@gmail.com]

onsdag 1 juni 2022 kl. 16:47:12 UTC+2 skrev timba...@gmail.com:
> Is 0.333... a valid number?

yes

> If so then by the structural argument the title's answer is yes.

Given it has finite number of 3s then yes, it is also valid.

If you meant ...33334 on the other hand with infinite 3's, then you are wrong and the two are not equivalent.

> The decimal place is obviously a structural augmentation to the natural value.

No, it is just notatoin.

> A long string of digits is all that is left to digest.

any finite number of digits is valid.

> Well there is slightly more. Are numbers two-sided?
> Isn't this cause to reject the usual decimal representation of 1/3 and insist instead upon:
> 1/3 = 0.333...3

Nope, stop being a crank.

> to secure the rhs? Now we have the initially built natural value though it is in an infinite form.
>
> To argue that the value of the digits are infinitessimal in the 1/3 instance does nothing to the informational representation. Likewise epsilon/delta will suffice just as it does for the irrational values as Dedekind presented it. The fact that the digits are redundant is handy. Still better if we went to modulo three representation one third would simply be 0.1 and so no puzzle even ensues.
>
> For those who like infinity I would think they'd like to let in this infinite value representation of a natural value.

They work in other number systems, just not reals. Educate yourself. look up p-adic numbers.

[Chris M. Thomasson]

On 6/1/2022 7:47 AM, Timothy Golden wrote:
> Is 0.333... a valid number?

[...]

Is this a valid number?

[0] = rand_range(0, 9)
[1] = rand_range(0, 9)
...

We can get:

.218575540978324672654

or anything else...

;^)

Each digit is a random number for the arity of the system. So base 10
(10-ary), 0-9 random numbers for each digit...

We can go for infinity... Is there a limit? Humm... No? ;^)

[Timothy Golden]

It is worth pondering the random digit value as you are trying to do. As well there are nonrandoms such as the irrational solution for sqrt(2.0) which arguably do have specific digits. The ones though which are already in use are the repeating decimals, and the usage of ellipses there works out consistently. To claim that every digit is well defined seems quite readily understood:
333...3546
as a valid constant infinite value shows we can easily work the tail of the value. Can it be said that:
333...3546 = 333...3545 + 1 ?
I think so. This appears to be valid. To state that
333...3546 = 333...3546
as well seems valid. If this were not so then there could be serious trouble. Somewhere along the way though as we push this interpretation something will break. Still, because the natural numbers are so primitively defined through the successor these values don't necessarily have to go through this much:
111...11134 + 222...21 = 333...355
though even this seems uncontroversial. Multiplication even somewhat can take on its full meaning, but this will not be so easy will it?
( 222...22)( 3) = 666...66
well, that wasn't painful, was it? With the help of sage, and the ever strange system of repeating digits which we generally gloss over I see that:
( 222...22)(11) = 2444...442
and no doubt that could be readily proven. Induction will probably serve us nicely here in the long run. Now for the jaw breaker:
(222...22)(333...33) = 740740740...740259259259...259
and so the first double ellipsis is born and as well a discussion of the number of digits exposes that with the multiplication we are duly representing the increase of the digits with the second ellipsis. If we are going to play in aleph land as A digits then we have 2A digits for this product.
So there is plenty to work on here.

It's not really my cup of tea, but I do drink tea from time to time. I even like to pick my own tea when I am doing well. Springtime is a fine time for raspberry and blackberry. You go home with your hands stained green and oily from the fresh shoots. Dry them on a screen in the attic and you've got a year or two's supply in a couple hours of work when the right patch is found.

To be convincing here we have to cover the ground, and Chris ,you are doing that. Possibly the correct random value is well defined at both ends so that a proper instance might be more like:
d1 d2 d3 ... d3 d2 d1
where d(n) is random. Is redundancy necessary? Redundancy in nature is well supported so at least there is physical correspondence. As to whether they are computable I can't really say. Here is a neat square:
(222...22)(222..22) = 493827160...493827160 49382 61728 395061728...395061728 4
Hmmm... There's a bit of confusion on my part as to how to write this. Multiple representations of the same value are not necessarily desirable.
Above I've compressed the usual tripling of the repeating sequence and inserted spaces for consistency.
Still, by sage induction I'm pretty sure this value will hold up. I checked it at three different levels this being the longest:
sage: 22222222222222222222222222222222222222222222222222222222222222222222222222
....: 22222222222222222222222222222222222222222222222222222222222222222222222222
....: 22222222222222222222222222222222222222222222222222222222222222222222222222
....: *2222222222222222222222222222222222222222222222222222222222222222222222222
....: 22222222222222222222222222222222222222222222222222222222222222222222222222
....: 22222222222222222222222222222222222222222222222222222222222222222222222222
....: 2
49382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617284

So for all that blathering about infinities and infinities of infinities it seems there could be quite a lot to do there.
I'd rather not actually, but since nobody else will I'll go ahead and demo it. I think possibly I am getting to the point of the grammatical meaning of 'of' within mathematics as a term of generalization. That's more to the point.

On the other side of the infinite instances lays the finite instances and they are plenty good. This long one up above is fine. Epsilon/delta functions long before we get this far. The rational value fails out of the gate. It is the decimal value and its unity interpretation which gets us the continuum. Pushing farther on unity interpretations we can have a bit more, but the dirty reradixer is trouble. As we agree by convention to work in one radix then to push another without explicitly stating it to be so is problematic. This is built into the nature of the rational value.

[Ross A. Finlayson]

These numbers of course with "many or slowly repeated a terminus, then a
different one for example zero", ..., "rational", is for roots it seems, powers
under roots or for primary functions, result measures, boxes, frames, ....

You then have them related this way, in terms of values, and either what
they parameterize or how they are parameterized, "numbers".

Here when you say radix, it's the representation also the fixed-point,
whether .111... is the radix or 1 is the radix, just to point out that the
term "radix" is overloaded, in terms of elements of the field or fractions,
and elements of the iota-values or increments.

... For example when the field is large, but finite.

[Timothy Golden]

There is something wrong with the square of 222...22. I put one extra 2 on each product from the long instance I gave and the middle nonrepeating digits turned from 61728 to 7061728. So it's not quite right there in the middle. It's been consistent other than that though.

Putting on one additional 2 I now have 715061728 for the center digits. Plodding along finally at
a=2222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222

we get clean and there is no middle digit conundrum. That's 226 twos. On intervals of nine twos. Perfect again at 217 twos.
Given the digital redundancies I think it is fair to claim that the square of 222...2 is:
493827160...395061728...4
where again I've compressed the notation down to something that is not so redundant but can be decoded given the earlier work. Given the extensive use of repeating digits this format is better. It happens not to need any spacing but space would allow say for a unique head in any position.

It seems like these infinite forms are getting more informational. There has been a process of reduction here that is not uncommon in other mathematics. We like to work with the simplest form and I believe I did prove it. possibly a formal proof would look a bit different, but the mechanics as stable here allow for induction to take place. There are eight other forms of this value and since we are in a weird new form could it be that there are nine squares of 222...2? Surely this is a side-effect of the radix that we work in. When we blame the value rather than the radix... well possibly that is when the dirty reradixer finds his way.

With ten twos (a = 2222222222) we see
a*a = 4938271603950617284
which is the first clean instance though no repetition occurs. Somehow this is a reduction of an infinite system worked in base ten.
Insert some ellipses in the correct locations and the infinite form is available; not unlike the insertion of a decimal point to beget the continuous value. I think as one starts into this infinite form we see that a new sort of grammar emerges. I don't think it is general yet, but it is emerging simply through usage. To state that these infinite forms are highly redundant is a necessary predicament, yet to which physical correspondence does hold.

It might merely be a place to get lost in. It might not be wise to entertain these things seriously, yet in the quantity of ground that could be covered these are possibilities. We have demonstrated an ability to square an infinite value here. The computation is digital in nature.

[Ross A. Finlayson]

Well if at the factory then the precision makes a real good rational
measure of 1/9 as about 1/3, say, then an analog computer could
be implemented with usual terms like geometric series, for example.

"If you're going to go about reinventing geometric series you
don't have to do so so publicly".

This example analog computer in what looks like your numbers,
a manual analog computer, is for that the "computer" results from
the 2's (or 1-9) at the front then zeroes, that the difference from
this results getting
.000 000 000 000 000 abc 000 000 000
from
.222 222 222 222 222 2+a2+b2+c 222 222 000.

... for more or less a direct form or representation of machine integers,
and operations on them according to "geometric series embedded
precision representation".

[Timothy Golden]

I do appreciate what you are saying here. I find I have to disambiguate it.
The wiki does point to 'root' as 'radix'.
That I think is the sweetest meaning, with our other usages more contaminated through convention.
This terminology of 'root' as literally in a plant structure the part which is underground seems very apt.
That every radix counting system is a radix 10 system is somewhat to blame. This then ambiguates the numbers that we are working in and that ambiguity with its side effects come out many times over.

For instance some will happily dissect the number as a polynomial form in powers of 10 as if they have done some great duty in declaring the meaning of those digits. Yet as they need more than one digit to do so these attempts are not simplifications. Particularly for instance to dismantle the value
222222222222
and assess that leading digit as 2 x 10 ^ 11 we've thence used two two digit numbers in our grand dissection. This is problematic. As to which comes first: the polynomial or the number? As to their shared properties: yes; these are of interest and particularly as we go at the roots of mathematics and perception of fundamental options in order to disambiguate these systems then such awareness is necessary. The dissection of number as a formality makes usage of the sum, the product, and the exponent in its simplest form. Yet the meaning of these operators is upon the number, so to invert this relationship rings false. Meanwhile the natural value was defined merely with an incremental operation. So long as one works in n; so long as I can instantiate n=22222222 as a working instance; then this divorce is a falacy. If you guarantee the divorce then no instantiation will be possible, and the work dissipates as verbiage. The mechanism of these digits as little wheels that spin round and round and occasionally interact is a more accurate form, and sadly the term 'ring' goes abused by mathematics. That our hardware implementations in fact do the same even at large scale is of interest I think. A 16 bit binary counter is a modulo 65536 system in unsigned format. But of course an exception occurs no different than the interconnection of the digits beneath. That is the carry exception, or at least flag.

Modulo awareness seems inescapable. Does this mean that our cosmology ought to engage in this same thinking? It does seem to be consistent with observation thus far. To what degree does the redundancy of the night sky hide the effect? When we look far enough is it possible that we may claim some observation of a wrapping of spacetime itself? Working this out is not trivial. Some are open to it. To engage a modulo universe is in some ways to relax these notions of infinity. Even as they can be allowed the compression of redundancy diminishes them.

If this were the case then our numerical format whether in hardware or on paper would actually be gaining in physical correspondence. Our locality still limits our observations, but relativity is in some ways even more intact in a modulo universe.

[Ross A. Finlayson]

It seems for figuring out identities that are in the "concrete mathematics",
either for the analog identities which are perfect while the digital identities
are often not exact "modulo" or are organized to neighborhoods in the
volume elements (pixels) what is usually "the digital fixed point space",
or in "neighborhoods of digital floating point values", about the long extended
precision parts of what can result from according to a geometric series
and "computing", what makes a fine imprint on a fine track with a constant
overall precision, from the analog "computing" (which is a, "single time step
operation" or "systolic", ...).

The "point-set" is a usual mental model of from some universe of points, or,
geometry's: is a "point-set" and any subset a "point-set".

The space is again both a model of scale and a "point-set", in the real-valued, ....

What I'm saying is "universe? must be infinite and continuous".

In the terms which are "space" and "time", ..., it's about the least model
that has everything in it.

This unified field theory is really coming forward under all the branches
of particle statistics and parastatistics, in the sense that "Quantum Mechanics"
is probabilistic the, "physical interpretation" the "mathematical interpretation",
that Bose/Einstein and Fermi/Dirac and parastatistics generally have also
then for "SR and GR, from GR as it were, and STR and GTR (derived) from STR as
it were", this also helps in reconciling the atomic model, in duality with waves,
and, a total complement in resonance: for usual attenuations like entropy, thermo
2'nd law, ..., which express expectations the, "statistical ensemble" (which from all
directions classical is classical in all directions, besides relativistic, quantum-mechanical,
..., modern emergent classical and super-classical).

[Timothy Golden]

For rectilinear solutions the modulo universe ray traces out one side of a cube and connects through to the other side just as if that cube were stacked again identically. So whether you want multiple copies or just the one cube is a matter of convenience. By definition they are one and the same cube. Likewise this fits relativistically in that should you opt to invoke relativity you can move the frame of the cube and the thing still works out. This is sort of handy in that as you want to verify that things work well at the 'wall' of the cube you can move the edge close by, walk through it, but what you see is that there is no problem with this format. This is the description of a modulo universe in rectilinear terms with no need of any additional dimension.

There is another form as well that is simplex based. The simplex itself does not pack space but the signon does. Establishing the simplex coordinate system as unit rays emanating from the center of a simplex out to its vertices we observe that their sum (the rays) is naught. This is the balance that established the geometry of the polysign numbers, and even the lowly real line fits this mold. Stepping in all combinations of these rays, so for instance in P4 we have -1, +1, *1, #1 we will trace out a signon. It happens to be a rhombic dodecahedron in this case. This general shape packs space and it works in every dimension. Going back down to 2D we will see the hexagon is the signon. Down in 1D a bidirectional segment is the signon.

Why should each of these shapes ( say the cube versus the rhombic dodecahedron) work out to the same physics in one of these wrapped universes? It is an interesting problem and it does seem as though great care should be taken when working on these forms.

Then too there is another that is quite attractive and that is the n+1 sphere, so that we are on a surface that mimics those modulo concepts somewhat. I believe this one has been worked on much more than the modulo versions. These all however are finite versions of the universe dependent upon how large they may be. You can have your conceptual infinite ray on them, but by the time you wrap around you'd have a fundamental figure. Our actual rays that do this are light, and so physics ensues.

Modern observations are claiming a finite aged universe, which means a finite sized universe by including the big bang.

If anything we ought to be open minded. These things are not done and dead and pickled yet.
https://arxiv.org/abs/astro-ph/0304558
I don't understand this quadrupole moment, but then, neither do they.
If it is wave theory in a modulo universe then we have two candidates at least.

[mitchr...@gmail.com]

On Wednesday, June 1, 2022 at 7:47:12 AM UTC-7, timba...@gmail.com wrote:

Why wouldn't a well defined quantity be valid?

Mitchell Raemsch

[Timothy Golden]

A less controversial solution exists on 333...3 whose square is:
111...10888...89
or in short spaced form:
1... 0 8... 9
and no controversy seems to ensue starting at a=33 where aa = 1089.

The effect of the product in raising the quantity of digits is something ignored in abstract algebra. They insist upon an infinite length polynomial to hide this, yet it is clearly a fake formality. To correctly account for their infinity of zeros after a product is taken there should be two sets of ellipses. Otherwise they've screwed aleph. So this numerical analysis does expose something beyond its own construction. If we bridge number theory at this primitive level with the polynomial and even into its abstract form the glue that binds these things exposes that infinite length strings are not only in use in higher mathematics, but they are insisted upon, particularly in abstract algebra.

Again a choice can be made to reject this usage or to go ahead with it. Each choice has consequences. Either way abstract algebra is broken.

[Ross A. Finlayson]

It's interesting what is "effective infinity" or the limits of precision, where any
point is both at the center of an oriented lattice, and of a sphere.

When you mention digital then there's Wolfram's massive "A New Kind of Science",
it's very much about the development of cellular automata, which in a sense describe
the same evolution in series but "always granular" instead of "ever fine".

[zelos...@gmail.com]

why do you do these discussions on constructions and things you clearly have no clue about?

[Timothy Golden]

Constructive freedom is such a fundamental concept that for you to shit upon it like this is only exposing your own short comings.
So long as you offer no content or falsification it is like talking to a vacuum cleaner.
Keep sweeping, Z.

[Timothy Golden]

a = 111...1
is pretty tricky squared:
123456790... 098765432... 1
and there are ambiguities in the middle along the way, but this is the clean solution.
The cube suddenly turns horrendously long:
137174211248285322359396433470507544581618655692729766803840877914951989026063100...
392318244170096021947873799725651577503429355281207133058984910836762688614540466...
470507544581618655692729766803840877914951989026063100137174211248285322359396433... 1

Troubling especially since embedded in the last repetition is the first repetition.

The NKS algorithm is awfully primitive. That does bring time into the discussion I think.
It seems like the mathematicians avoid time. So do the cosmologists. Their first principle is that space is isotropic; not that spacetime is isotropic. So does this mean that spacetime is structured? Nice discussion they are not having on this.

What is good about NKS is emergence. At the early stages we should accept any emergence as progress so it deserves credit. At some point we want to demand emergent atoms with the exact spectroscopic properties, exact isotopes, and so on as we witness in nature. As to how much of physics is sitting upon empirical data: this limits how far theory can get. Theory is lagging way behind experimental physics. This position rejects curve-fitting as theoretical.

If we establish an emergent form of spacetime then isn't there cause for hope?

[Ross A. Finlayson]

Sorry if as soon as I couldn't understand at all I immediately lost interest, ....

I think it's more that "hope for emergent space-time" is anthropic,
which is great, also that it's manifest, ("emergent space-time is, ...")
which is fine.

It can't really be emergence, without, convergence.

[zelos...@gmail.com]

There is nothing to refute with yours because it is not even wrong. It is word sallad.

You show 0 understanding how number construction works in mathematics. So you have nos ay in the matter.

[Ross A. Finlayson]

What do you mean when you say "mathematics"?

Number theory?

Theories of mathematical objects are great because it doesn't
matter for their function, any other theories of mathematical objects,
at all.

Foundations of mathematics of course is then a theory of all mathematical
objects, more or less.

If you think that "number construction" is only "algebra 301",
"according to Galois", ..., not necessarily: that's just a linear
narrative, so linear thinkers in a linear curriculum don't need
to relearn more than some simple data structures preliminaries,
up to basically the fundamental theorems of arithmetic and algebra.

See here he's basically defining those ..., "numbers", himself:
and is free to do so however much their definition defends itself.
(That it's "mathematical".)

[Timothy Golden]

Infinite fours 4...4 squared:
197530864... 580246913... 6.

The anthropic principal is terrible. You might as well go back to earth, wind, and fire as your basis.
Actually the anthropic principal is even worse because it reads more like:
"It is the way it is because that is the way it is",
which is no theory at all.
When humans got to (x,y,z) coordinates they did something good. Still, this is an empirical match. Empirical lineups are at least better than anthropic backboards, so maybe I had better stop picking on the empricists so much. In such comparisons it is looking more and more like mathematicians are somewhere between religion and science. They don't give a damn about either, but they do love their book. I no longer accept the mathematician as having attained purity. Claims of perfection are overstated. Ambiguities have been passed down and absorbed; trained into us under threat of failure. You have to stop bowing and start constructing. Cover some new ground. Cover the old ground a new way. I'm not saying that mathematics is doomed. I'm saying that we are in a progression that has not finished. From a blank slate is how we got here. If we had a message from a god that would be wonderful, but we do not have any such thing afaict. It's the blind leading the blind I'm afraid. Occasionally out of thin air something new comes up. Then too there is the problem of accumulation. Consider the professor who has heard the same complaints about his topic from fresh intelligent students every other year for nearly half a century to the point that he instinctively gets excited, starts waving his hands and diverting the class onto a more complicated conundrum in order to wipe out the simple analysis that should have ensued. Living the lie never quite felt so real did it? And the poor students always looking for the high grade... the one who walks away will never know how good he had it. So do jump through the hoops, but call them on it too. At some point the mimicry is gimickry. Calling this civilised... hmmmm... I'll have to ponder that.

Let's see now.... ten Nazis and a Jew show up at your doorstep looking for contributions for the war in Ukraine and you think to yourself:
"These Nazis must be a-ok if they are hanging out with a Jew." You open your wallet and hand all your cash over to the Jew. The Jew hands the money to the chief Nazi who is pleased and jokingly because he is an old comedian the Jew says "cha-ching!" to which the Nazi says "yaddah-yaddah-yaddah", snickering, "You gotta love civilized society."

The fact of polysign numbers is a short proof of this state of mathematics, for they should not have been overlooked for this long. It appears that humans have a predilection for binary symmetry. Achieving n-ary symmetry is somewhat what polysign does; though it is working in numerics it results in geometric correspondence. It is a new path to the general dimensional and it is general dimensional out of the gate. We do not ask that two or three copies of the same thing somehow deserve respect. Thus they yield tremendous flavor. Emergent spacetime is near at hand at last! They are at your doorstep, sir.

[Ross A. Finlayson]

No, no, "anthropic" was co-opted as "mis-anthropic" this is original "anthropoticity".

The "anthropic principle" is not necessarily at all as of "anthropic perspective".

Let's split logic and leave room for an anthropic observer,
as only _technical_ philosophy, avoiding the "non-technical"
or "judgmental" philosophy, then for the usual key also of
taking "objectivism", away from "Objectivism", where in the
philosophy the "objectivism" is a neutral anthropic observer,
in terms of consideration and so on.

Duns Scotus was a great platonist, and not a neo-platonist.

As much as there are numbers they're "forms", ....

[michael Rodriguez]

Tim, still I am waiting for some tetrogonal frequency division multiplexer

https://en.wikipedia.org/wiki/Orthogonal_frequency-division_multiplexing

Best regards ;)

[zelos...@gmail.com]

I mean the entire field of mathematics. There are ways you go about constructing number systems rigorously.

[Timothy Golden]

Good to hear from you. Sorry I've let my website go... my email too. I may try to get them going again. I don't know.

OFDM is old technology now. So is usenet. Kind of fun. I grew up on a three party phone line here. If somebody else was on the line you'd hang up and try again in ten minutes. Each party had a different ring when a call came. We had two short rings. Not terribly private. We always respected it though.

It sure would be nice to predict something in the progression past electricity and magnetism as a result or consequence of a polysign basis. That could yield the sort of thing you are talking about. Whether that physics would show up in a twisted triple as opposed to a twisted pair: I guess it could be something to ponder. Then too in wireless form a tetrahedral antenna could yield something. Go from the dipole to the tripole and onward to the quadrupole antenna.

Getting back to exercising the infinite numbers, the square of 3...34 is:
1... 5... 6
but whether that should actually read:
1... 5 5... 6
could be relevant. Two ways about it: these product forms should conserve digits and in that numbers are always two-sided the 1... should have a tail. Whether its tail is one or five: I'm leaning on other examples for the moment so for instance when a = 3... 2 the square is:
1... 0 2... 4
Whether this is murky ground or simply equivalent representations I am unsure. I do still think the whole business is murky. Still to outlaw these infinite digit strings would be to outlaw 1/3=0.333... and I do think rather a lot are still in favor of this one. After all, the prior compilers have approved it, right? The radix point as structural demands attention. Unity and its various adjustments in numerical notation deserves consideration. Wouldn't it be nice to recover a clean form of the rational value since it lays broken? Breaking the back of the real value; I never thought it would come to this. Still, here it is, drowning in digits. By the time the engineers, the physicists, and the mathematicians come together on the proper usage of radix point notation the mathematicians will be insisting that every real value they ever spoke of demands 000... on the end. The proper conversation lays back on the continuum with this really merely a diversion.

[Timothy Golden]

I do think that the human position in all of this is relevant. But I go in a different direction with it.
For instance in talks on human consciousness there is great trouble as we dodge human programmability.
The programmable human is the greatest problem that we face.
Our schooling is programming. It takes many years of it to be done with it.
Coming out the other end it is the best mimics who make it through.
Those whose minds were working on variations and so couldn't keep up with the lectures fail.
They are weeded out and so academia breeds automatons.
You can listen to any of the leading physicists spout out the same interpretations of the subject.
You can only step out of line so far before the system as such utterly rejects you.
Anyway that's a lot of down talk. The other side of the coin is that without the mimicry we would all be starting from a blank slate. How far would we get? Not very far. Just to utter a few words and have them shared in your family would be enough I suppose. There is no guarantee that the accumulation as it has gone down is correct. The fact that we are swamped in accumulation is problematic. All the cross linking in the world will only add to that accumulation.

Anyway as humans we are conglomerate elements of spacetime. Our access to the fundamental properties is suspect as such. This at least helps explain our long struggle to understand. But beyond this as you ponder academia and witness the slow progress and false starts then we are witnessing the human condition. The most positive aspect of this position is that I can firmly declare that the system is open for future contributions.

The anthropic principal strikes me as egotistical. The same mistake has been made many times over in history. The Abrahamic religions grant some exclusive properties to their followers; Free will as a human right from the philosophers; Nationalism as a guide to which every public school child swears its allegiance daily; these are all grabs of the human identity. Possibly the same could be said of globalism, but as far as we know the buck stops there. How physics claims that the human form is relevant seems next to impossible to me. Those little whirring micromachines that process our DNA into RNA and so forth are mystifying. We know that our form is arbitrary by evolution. Possibly the anthropic claim simply dissipates to the empirical all over again. That is a zero gain position. We are just simply back to observation, which you are pretty aware of based on your own language. Still, as human observers our position and scale has to be understood as limited rather than as overarching.

[Ross A. Finlayson]

One of the strengths of intuitionism over constructivism, is that
intuitionism posits properties of objects to apply in inference, while
constructivism is more blind of all but the "proper" (defined) axiomatics.

Here then "Tim's numbers" you find lacking a didactic, fundamentally
axiomatic, platform or foundation, but, he's just describing properties
of the objects of his interest, then with the notion that given all the
other objects of mathematics, that they eventually share common relations
on the most common objects of mathematics, which here are integers and
real numbers and their Euclidean/affine lattices.

Then, you're welcome to go about showing how given common relations
of other objects that these objects ("numbers") are somehow inconstant
or otherwise make for a contradiction, and welcome to defend the common
features of "usual" or "our standard" definitions of objects of mathematics,
but troll+anti-troll = troll and crank+anti-crank = crank.

So, intuitionism assumes a great context of mathematics as objects, and
mostly all of them, and constructivism is very much "the least chain of
inference that arrives from the least relations to the least inference,
thusly least-loose", but at the end of the day for foundations it's "by definition"
to be both, constructivist, and intuitionist, because "objective" and "subjective"
apply in various conditions to either, ....

[Ross A. Finlayson]

I'm hoping that for the "anthropic observer" as a general notion of the
"abstract anthropic thus objective, observer", that it's key that the anthropic
is a consciousness, that the "anthropic principle" or otherwise "us first" has
that the anthropic just refers to the conscious, and free of will, not the
"suffering and aggrieving the human condition, justified by some non-anthropic" .

I.e. this is the philosophical anthropic, "man as spark of consciousness",
not the political anthropic, "man as master of animals".

[Ross A. Finlayson]

Consider for example this recent article about Arnold conjecture,

https://www.wired.com/story/mathematicians-transcend-a-geometric-theory-of-motion/

"These computations are typically done using the integers,
or whole numbers. But they can be done with other number
systems, like the rational numbers (those which can be expressed
as fractions) or cyclical number systems, which count in circles like a clock."

What do you make of these, "cyclical number systems" or clock arithmetic?
How about if they are infinite and look like "infinitesimals [0,1]"?

A metrizing ultrafilter looks just like "infinitesimals [0,1]", ...,
for the intents and purposes of real analysis as it were
infinitesimal analysis: it is. Some people have that fundamentally
or primarily that the "real object" is "continuum [0,1]", not
"duck-typed the same thing and please don't point out that
rigorously it would suffer the same immediate contradiction
as the initial object clock-continuum [0,1], itself".

Instead of course there's for resolving such contradiction with
the existence of the particular special pre-Cartesian clock-continuum
in an extra-ordinary set theory, so that all the replete features of
the continuum are put up front instead of not being "fully conscientious".

Or "conscientious formalists 24/7".

P.S. mathematics _owes_ physics real mathematics of infinity.

[Timothy Golden]

Well, or does mathematics owe physics a modulo playing field?
I did try to understand the link, and went to a very complicated paper off of it.
Technology has made it to the 64 bit machine.
Suppose we had a reference space (x,y,z) in three of these 64 bit values.
We don't have this sort of memory resource, but we can have a list of objects containing such positions.
These values wrap so that physics done near the edge simply works over to the other side.
For instance a map of such a space with an object on a trajectory that crosses y=0 from the right lands that object at y=ffff...ff (in hex).
You see no work needs to be done in this case. I think the question is: what prevents this from being the sort of universe that we inhabit?
Already on a 14 billion light year universe the resolution is 0.2 meters.

I think the point would be though that we may have a smaller universe and we are looking at wrapped images of it. Is there any reason that we should recognize an object that is 1 billion light years old? Already at a billion light years away we will be quite lost won't we? This is the simplest of cyclical spaces. Maybe that is the crux: suppose we see our sun (good luck); our galaxy at a billion light years... how would we know it?

You 'd think Tegmark would be done with this one already; after all this is pretty much the model of a lot of cheap video games.

I am not a cosmologist so I can't speak to how many metrics on galaxies they have. The simplest point is to realize that in our local space nothing is offended by this model. If anything relativity and the lack of an observable origin are compatible with this model without augmentation.
It is a strange container but I find it believable. I can't characterize how such a cube behaves versus a rhombic dodecahedron versus a 4sphere shell.
Because they are the universe possibly this problem goes away? In this way even calling them by these shapes would be a misnomer. This is the level of care that has to be considered as we discuss this level. Also time is left out. Expansion is left out. I'll admit it is awfully simple. The 64 bit value is oversimplified, but in a pinch it'll do. I'm still a believer in continuous space. And emergent spacetime.

Yes, cyclic is very good.

[Chris M. Thomasson]

On 6/8/2022 5:57 AM, Timothy Golden wrote:
> On Tuesday, June 7, 2022 at 5:58:56 PM UTC-4, michael Rodriguez wrote:
>> Tim, still I am waiting for some tetrogonal frequency division multiplexer
>>
>> https://en.wikipedia.org/wiki/Orthogonal_frequency-division_multiplexing
>>
>> Best regards ;)
>
> Good to hear from you. Sorry I've let my website go... my email too. I may try to get them going again. I don't know.
>
> OFDM is old technology now. So is usenet. Kind of fun. I grew up on a three party phone line here. If somebody else was on the line you'd hang up and try again in ten minutes. Each party had a different ring when a call came. We had two short rings. Not terribly private. We always respected it though.
>
> It sure would be nice to predict something in the progression past electricity and magnetism as a result or consequence of a polysign basis. That could yield the sort of thing you are talking about. Whether that physics would show up in a twisted triple as opposed to a twisted pair: I guess it could be something to ponder. Then too in wireless form a tetrahedral antenna could yield something. Go from the dipole to the tripole and onward to the quadrupole antenna.

[...]

Fwiw, check out these interesting fractal antennas:

http://www.fractenna.com

https://patents.google.com/patent/US6452553

[zelos...@gmail.com]

again, have you ever bothered to study how number construction works?

[Timothy Golden]

Yes. These are wide band or 'diversity' antennas. It's pretty crazy how many bands the phones are working with. Maybe one day the FCC will reign them all in; back out of the auctioned wavelengths, and enforce real standards on what is a cutthroat capitalist environment. Still, the technology works and has been life changing. Look around any coffee shop to witness that.

I haven't tried this modulo approach on fractals yet. Nobody seems to have picked up on the pure orbitals either. Somebody should really have a go at this. Some sort of moire could show up. On the other side though, there is a long standing problem with our fractal mathematics: As you choose your image points based upon an escape criteria the ultimate image is formed by the edge of escaped versus nonescaped points. This is a critical zone. If we use an iteration level of 10,000 iterations on
z[n] = z[n-1] z[n-1] + z[0]
then we have a product that has lost a tremendous quantity of digits. Thus there must be some error from the perfect form and thus the edge must be incorrect in the graphic. Here the analysis gets tricky, but I may have a lead on how to investigate this. Oddly enough it occurs at low resolution and at low iteration; otherwise the perfect product cannot be found. This could be done for a complete image say on a 256x256 grid. If an error shows up there then shouldn't that error be as pronounced at higher resolution? Then too a few points might be possible at high resolution. Roughly a 32 bit value multiplied by a 32 bit value will yield a 64 bit value in general terms, so that the final multiplication in a 10,000 iteration product will be 320,000 bits. Of course we are interested in the edge of that graphic for this is where the corruption will be observed, and at this edge small changes matter. These are largely harmonic patterns with various z[0] being drawn into the same attractors by the rotational product, then offset by the original z[0].

There may be a crossover to these infinite values simply based in long digit strings, though the perturbation by z[0] is not going to make that easy...

z[1] = z[0]z[0] + z[0]
z[2] = ( z[0]z[0] + z[0])( z[0]z[0] + z[0]) + z[0]
z[3] = ( ( z[0]z[0] + z[0])( z[0]z[0] + z[0]) + z[0])( ( z[0]z[0] + z[0])( z[0]z[0] + z[0]) + z[0]) + z[0]
z[4] = (( ( z[0]z[0] + z[0])( z[0]z[0] + z[0]) + z[0])( ( z[0]z[0] + z[0])( z[0]z[0] + z[0]) + z[0]) + z[0])(( ( z[0]z[0] + z[0])( z[0]z[0] + z[0]) + z[0])( ( z[0]z[0] + z[0])( z[0]z[0] + z[0]) + z[0]) + z[0] + z[0]
z[5] = ((( ( z[0]z[0] + z[0])( z[0]z[0] + z[0]) + z[0])( ( z[0]z[0] + z[0])( z[0]z[0] + z[0]) + z[0]) + z[0])(( ( z[0]z[0] + z[0])( z[0]z[0] + z[0]) + z[0])( ( z[0]z[0] + z[0])( z[0]z[0] + z[0]) + z[0]) + z[0] + z[0])((( ( z[0]z[0] + z[0])( z[0]z[0] + z[0]) + z[0])( ( z[0]z[0] + z[0])( z[0]z[0] + z[0]) + z[0]) + z[0])(( ( z[0]z[0] + z[0])( z[0]z[0] + z[0]) + z[0])( ( z[0]z[0] + z[0])( z[0]z[0] + z[0]) + z[0]) + z[0] + z[0]) + z[0]
...

The imagery is still excellent, and clearly we owe most of it to our hardware processors, but already here at z[5] a tremendous amount of the original intent has been thrown away. The edges are on the order of z=2, and at z=10 we are well escaped. The portion that has been thrown away is admittedly small, yet we are going to find the edge of this thing and that is just where that small amount will matter. Well then should it be enough merely to compare a 64 bit process against a 32 bit process? There is a simple enough problem. Somebody must have done it.
Didn't find it but this is a pretty good find: https://www.acsu.buffalo.edu/~adamcunn/downloads/MandelbrotSet.pdf
It does try to do some error analysis.

[Ross A. Finlayson]

The "modulo playing field" is usually called "having a metric".

The infinities are more like "this vanishing effect starts as an infinitesimal".

It's part of where the "Democritan regime" or "Planck regime" rules at
the scale of atoms and Planck's constant, that what is continuum analysis
is modeled as a large number of discrete elements, "if not effectively
infinitely-many", why mathematics owes physics more and better mathematics
of infinities and infinitesimals. Then, besides continuum analysis, is about
where things differ infinitesimally where there is no "symmetry-breaking",
that a wave resonance arrives at some "symmetry flex", what these days is
being studied for example as a field the "quasi-invariant analysis", where of
course physics otherwise offers already the "invariant analysis", what is validated
by Big Science these days the predictions of relativity and QM to some 25 degrees.

[Ross A. Finlayson]

You menion harmonic and it's really key, for the harmonic and anharmonic
that the harmonic frequency analysis, in constructive interference, just like
wave equations for periodic intervals - it's really key.

Overtone, ....

[Timothy Golden]

Well possibly this does work into a modulo universe as well. You seem to not want to worry about a ray trace that wraps back through the same space. I am concerned about this feature and wonder if it could be detectable. If ordinary electromagnetics hold up, and I would think we would allow that then the delay is the problem. Possibly the correct analysis is to start small and work up toward a less detectable size. If the big bang interpretation is correct in that spacetime is generated at the big bang then this small size universe did once exist. In a modulo universe the size of your house you should be able to turn on a flashlight and witness the effect. Turning on the light for ten seconds, then turning it off, how bright will the room be? Did the brightness accumulate or was there wave cancellation? Were this done with a red laser would the result be different? Catching the first beam seems simple enough: shine the light behind your head and you should be able to sweep your face with it. Hold the light off to the side a bit and you should be able to get multiple images of it. Maybe put some smoke in the room to get a better feel for these effects rather than shining a bright light directly into your eyes.

There are claims that the first appreciable informational radiation from Earth was the 1936 Olympic games in Germany. Let's say this radiation reaches us in 2036, so that would then establish the 100 light year span modulo universe. Attenuation will be problematic. This being the first wrap of the signal it seems likely the wavefront would come cleanly just as if there were another identical Earth 100 light years away. Maybe this simple analysis breaks the modulo universe: now look in any direction at 100 light years and you'll see Earth. True? No. That's the spherical model. So there is a distinction. Simplifying down to a 2D box there are four direct images of Earth and they will be orthogonal. Then there will be four more on the diagonals at 45 degrees to those first four, slightly more distant. Then more and more, and I suppose yes, in every direction there will be an Earth, but many are more distant thamn the others. So to focus on the closest images will be the most direct. In the 3D box model (Cartesian) there will be six. In The P4 model (polysign signon) there will be 12 of the shortest path based on the 12 faces of the rhombic dodecahedron.

These are a bit oversimplified in that we haven't placed any other objects in the universe, or maybe call it a chamber? We seem not to worry too much about occlusion but it could be a factor. These preferred directions would fly in the face of isostropy. Still this is working on the presumption of observability. Ahhh. Maybe there we have it: a supernova from eons ago shows itself from many positions in the chamber universe. Errr... When we catch these we happen to be in the jet don't we? On to cepheid variables perhaps? Really we'd like to break the model as quickly as possible. Somebody must have something. I could swear I remember reading claims of directional poles in the cmbr rather than wavelength based poles. I forget who that was now.

[Ross A. Finlayson]

The ray-trace is right for geometric light, but there's also the optical.

Consider for example sketching a sphere in perspective, where
the shading marks are basically drawing shade, not light.

Fritz London was a theorist who much expounded on superconductivity.

It's kind of like the pilot wave / ghost wave - collapses everywhere at once, ....

These days it's back in fashion that "the wave equation and wave collapse does
have a real interpretation", vis-a-vis what was some "dither, ...".

[Timothy Golden]

I do remember one strong interpretation (can't remember his name though) that insisted that just staying with the wave form was correct.
I sort of get it. But why these waves do not dissipate I don't get. As well I have seen on calm water little discrete wavelets. Sometime near calm water watch closely and you may observe them.

To formalize my qualm let's call it the stability problem. Why are electron waves so stable? I remember doing the Millikan oil drop experiment in college. You spritz into microscope view oil droplets which have picked up some static charge during the spritzing. Pick one and vary the voltage on the power supply until it goes stationary. jot down the voltage. Repeat. Repeat. Repeat... graph the voltages. A staircase of Discrete levels ensue. Actually maybe they were teflon balls rather than oil drops. Someway along there you get a raw value for Q(e).

We are dealing in intangibles at some level as we go down the chain into the small scale and the fundamental. To what degree the reductionism that we are working through is correct would sort of form a fresh lens to step out away from the system. The physicists do generally bow to the mathematician's real number. Einstein certainly did. Maxwell did. I could happily sit back and address these two-signed morons in hindsight, but I haven't completed the replacement theory. I've got a strong start though. Simply put generalize sign, sir. You'll find it does wonders. The history of mathematics exposes just how slow wee humans actually are. As creatures of habit the act of mimicry should be more carefully exercised. The burden is on the next generation and it will always be so. The answers could be sitting underneath all of our noses and we've simply habituated an assumption that is not valid. Our system is buggy. Let's at least own that.

Beyond this to eat things like particle/wave duality is very much like Nazis bedding down with a Jew. To admit that something doesn't feel quite right, so let's send them some more money... Right? I guess if it involves sending all of our Nazis over there to be slaughtered by the Russians then I could be OK with it. Maybe this is what JB has in mind. There is an oxymoron. Time for the pushup contest.

[sergi o]

Nazis ? pushups ? WFT ? please disconnect your computer from the internet, it is vomiting forth spewing fake sciency drivalings

[Ross A. Finlayson]

Static electricity - in those days the most fun we had
was rubbing a balloon then attaching it to a cat.

Combs and little pieces of paper, ..., "fun with static electricity".

You know I used to be able to scuff my feet and zap my desk,
now it's "electro-static discharge" everywhere, ....

I studied Ampere and about power electronics and digital electronics,
Ohm law Kirchhoff law, circuits, networks, most of my electrical thinking
is systolic in the sense of "this clock chip drives these electrical inputs
which systolically flow through others in junctions which according to
timings result symbolic logic", compared to "these high-voltage transmission
lines run electricity from this dam to all these people".

Particle/wave - helps resolve that "according to atoms this is grainy but
according to geometry this is smooth, and grainy and smooth represent
the entire mathematical notion of discrete and continuous".

Then, particle/wave/resonance(s), helps to explain "these are yet waves, ...,
while organized as about a space-time".

This though is where "the 3-D space + 1-D time is the only way so
organized a space-time", the space.

Then there's for all matters of projective and perspective, everything in its place.

[Timothy Golden]

Your knowledge of current events suggests to me that you are a mainstream media stooge.
That or you are a monk.... or a monkey.
How about doing some math?
Is there a problem with:
x = 333...34
4x = 1333...36

What right do I have to claim that 4x > x ? I could claim its validity, and possibly I could claim something about aleph and those ellipses. But to claim that
33333...3 > 333...3
seems ambiguous. This is all under development. I do know that the 4x computation above holds up fine. I do believe it should be true that 4x is much greater than x. The question then is whether the numerical representation can account for say aleph plus one digits. Pretty sure normal theory on infinity does not like this. It is true that in the infinite products such as
x = 333...34
x*x = 111...1555...56
that the two sets of ellipses matter, but now we are coming down to accounting for the quantity of digits in the heads and tails of the strings. I have not been very careful and that last value above here looks out of balance. As to whether there is a missing one or a missing five in the middle I don't know at the moment.

It seems quite believable that
111...1 < 222...2
but now multiplying by ten the first value is it true that:
111...10 > 222...2 ?
Is the numerical representation going to hold up here? I think I may have some errors in my prior computations if this is the case.

I'd rather still side on the whole system of infinite length numbers being bogus, except some of these computations are working out. Apparently they are disproving some of WM's claims on dark numbers. For instance these value have clean successors whereas he claims his darks do not. As far as I know these are the first infinite constants compiled by humans. You'd think that for all the love of infinity that goes on here on usenet that there would be more interest and opinions. Instead everybody dodges these. The usenet dodge remains an aspect of human reality that is underappreciated simply for the fact of its vacuousness. How many receive such treatment in our culture? Oh. Very many. Welcome to the club. I think it is best kept in jest rather than in gest. It's almost like calling up the breakfast barf club all over again. If nobody is willing to take any freedom of construction then how are we going to progress? At this stage and in this medium even a digression is worthy. Falsification is analysis. It is necessary exercise.

[Timothy Golden]

On Sunday, June 12, 2022 at 5:38:37 PM UTC-4, Timothy Golden wrote:
> It seems quite believable that
> 111...1 < 222...2
> but now multiplying by ten the first value is it true that:
> 111...10 > 222...2 ?
> Is the numerical representation going to hold up here? I think I may have some errors in my prior computations if this is the case.

The point of a construction is to make the construction work. As such even though I am in disbelief of it, computability forms the basic crux of this system working.
As such 10x > x should be possible and is possible, but it means that aleph plus one digits has to be let in. So for instance if we have
x = 111...1
and 10*x = 111...10
then this additional digit does put the head digit one past the x value's head digit. We simply would line them up vertically, presume the '...' to include identically many digits, and proceed with computations. Unfortunately sometimes we wind up with things like
x*x = 123456790... 098765432... 1
and now we will have to realign x to preserve digits. The digit sequence is correct yet interpretation of it under this lining up method is not workable. We could possibly introduce aleph markers so that lineups can be done without lining up per digit. As such we could augment each value with a bar | that indicates aleph so for instance
x = | 111...1
10 x = 1 | 111...10
x * x = | 123456790... | 098765432... 1
and that is quite convenient in that the added tails don't have to be worried about this way.
So I guess even though I did just expose some conflict the system could carry on with this bit more notation.
This really relaxes the cube of x:
| 137174211248285322359396433470507544581618655692729766803840877914951989026063100...
| 244170096021947873799725651577503429355281207133058984910836762688614540466392318...
| 951989026063100137174211248285322359396433470507544581618655692729766803840877914...

It gets quite difficult finding the fourth power. Somebody with greater persistence will get it I'm sure.

[Timothy Golden]

On Wednesday, June 1, 2022 at 10:47:12 AM UTC-4, Timothy Golden wrote:
> Is 0.333... a valid number?

> If so then by the structural argument the title's answer is yes.
> The decimal place is obviously a structural augmentation to the natural value.
> A long string of digits is all that is left to digest.
> Well there is slightly more. Are numbers two-sided?
> Isn't this cause to reject the usual decimal representation of 1/3 and insist instead upon:
> 1/3 = 0.333...3
> to secure the rhs? Now we have the initially built natural value though it is in an infinite form.

It always was an infinite form. This construction requires some adapting to, and why is this? This is simply because our mimicry does not account for generalization. Our mimicry as much forms bounds on our style as it requires regurgitation. As to when the logical bounds of the mathematician are in conflict versus the bounds of mimicry being crossed: as slightly better than monkeys it is not for us to say. As to how many openings like this exist in mathematics: here we do engage our monkey skills as Shakespear's monkeys. At that point the logical filters have to kick in and reject rather a lot of nonsense. If your filters reject this form then it is you who I would like to have a discussion with on this topic. The value 333...34 is an inductive form. It felt foreign to me as well. To admit that this value is merely a representation exposes the myths and the magic in mathematics. That the number itself can encapsulate the inductive step is exactly as the standing mathematician views his real number... without the ellipsis usage. For instance the man who utters "one third" means exactly that, and not even a slight error accounted for. As the same says "two" what they literally mean when they've jumped the naturals and stopped in at the real line, as if the naturals occur there somehow ready to go in some subset, what he really means is:
2.000...
and every zero matters in his opinion though he doesn't care to state any of them.

Is 2 = 2.000... true?

In a very serious way this question is connected to the first. As to who is abusing their numeric form: it is not the engineer nor the physicist. It is the poor mathematician who is abusing their numerics. Dragging us all into probabilities at such an early stage; yes. Every real value is trailed with an infinity of zeros; other than the forms that trail in something else. Every real number has infinite precision. This is the mathematicians perfect continuum. Working on that continuum we find practically that to achieve say 1.001 inches is very good precision in metals. Then again to get to the next level:
https://www.youtube.com/watch?v=sFrVdoOhu1Q
and of course the mathematicians have already gone beyond all of this in their form, right?

So ultimately though they may go 'mum here, they have legitimated the infinite forms, limited as they may be, long ago when they formed a notational convention that goes in direct conflict with physical reality.

>
> To argue that the value of the digits are infinitessimal in the 1/3 instance does nothing to the informational representation. Likewise epsilon/delta will suffice just as it does for the irrational values as Dedekind presented it. The fact that the digits are redundant is handy. Still better if we went to modulo three representation one third would simply be 0.1 and so no puzzle even ensues.
>
> For those who like infinity I would think they'd like to let in this infinite value representation of a natural value.
>
> For those of us who do not like this form we should then reject it as well back on the accepted repeating decimal result of the 1/3 computation. The augmentation of the radix point to the natural value exposes a special representation that is not taken seriously by mathematics so long as it is regarded as the rational value all over again. It is not. The division operation has been removed. A new unit value has been achieved.
>
> As we approach this play on unity with fresh eyes we could even push it farther so that a new unit position of say 123 is enforced. Of course what we will have is the concept of the rational value, except no division is necessary. Now we have a counting form of the rational value. This is apt I think. Addition is far more fundamental than division. Also though this concept of unity as bridging to the concept of unification through unitization raises the lid on an otherwise closed down and done thought process. At the bottom of it all is the modulo number. the 123 as a unit instance is nearby to a reradix, sir.
>
> These issues of course bleed onto the continuum and what we mean by it. What we even mean by countable can be broken down but for the mathematician's pure form of it in the natural value. Here now I come to wonder if even that form is undeserving of its name. Rather than 'natural' these ought to have been called 'perfect' or some such, 'exact' perhaps. 'Discrete' is pretty good though a bit more generic. Nature is far more tricky than the natural number. Reality versus the real number; well; you'll need three of them at least. Is each one then a third of reality? I do mean to belittle the terminology because deference to the past assumptions is likely partially to blame for the bottleneck that we are facing. As you bow to the masters who came before in a long chain of masters who bow to their masters your own mastery is suspect I believe. To cover the ground in a new way could be instructive particularly if we arrive at some new options.
>
> Under the structured approach, as we legitimate the radix point as a data structure, sign comes next. There I already have productive results. Here I cannot say yet. There is movement at least in terms of interpretation, and the fact that interpreting the unit could hold this far is encouraging. The rational value as broken has been established already. That I've come around to a new form of it through the unit interpretation feels pretty good. Best of all we are back to incremental counting and modulo principles. Exactly how polysign took off. Exactly how digits work. Spacetime is structured. Whose job it is to get it from thin air: will physics ensue directly? Should our concept of number get us here? Wouldn't this actually be the real number? Has mathematics taken itself hostage through its nomenclature? What an accumulation has occurred, and for those who manage to map it all like the lines of a bible; well; have they really done themselves any favors? When does simplicity cut in? Where does complicity leave you? I so must insist that I am not complicit with the actions of my government. To see through the eyes of a juror who bought Russiagate and in the midst of near nuclear war should a few mistakes happen... Sussman is off by propaganda alone. Triple down...

[zelos...@gmail.com]

onsdag 27 juli 2022 kl. 14:45:00 UTC+2 skrev timba...@gmail.com:
> On Wednesday, June 1, 2022 at 10:47:12 AM UTC-4, Timothy Golden wrote:
> > Is 0.333... a valid number?
> > If so then by the structural argument the title's answer is yes.
> > The decimal place is obviously a structural augmentation to the natural value.
> > A long string of digits is all that is left to digest.
> > Well there is slightly more. Are numbers two-sided?
> > Isn't this cause to reject the usual decimal representation of 1/3 and insist instead upon:
> > 1/3 = 0.333...3
> > to secure the rhs? Now we have the initially built natural value though it is in an infinite form.
>
> It always was an infinite form. This construction requires some adapting to, and why is this? This is simply because our mimicry does not account for generalization. Our mimicry as much forms bounds on our style as it requires regurgitation. As to when the logical bounds of the mathematician are in conflict versus the bounds of mimicry being crossed: as slightly better than monkeys it is not for us to say. As to how many openings like this exist in mathematics: here we do engage our monkey skills as Shakespear's monkeys. At that point the logical filters have to kick in and reject rather a lot of nonsense. If your filters reject this form then it is you who I would like to have a discussion with on this topic. The value 333...34 is an inductive form. It felt foreign to me as well. To admit that this value is merely a representation exposes the myths and the magic in mathematics. That the number itself can encapsulate the inductive step is exactly as the standing mathematician views his real number... without the ellipsis usage. For instance the man who utters "one third" means exactly that, and not even a slight error accounted for. As the same says "two" what they literally mean when they've jumped the naturals and stopped in at the real line, as if the naturals occur there somehow ready to go in some subset, what he really means is:
> 2.000...
> and every zero matters in his opinion though he doesn't care to state any of them.
>
> Is 2 = 2.000... true?

yes

>
> In a very serious way this question is connected to the first. As to who is abusing their numeric form: it is not the engineer nor the physicist. It is the poor mathematician who is abusing their numerics. Dragging us all into probabilities at such an early stage; yes. Every real value is trailed with an infinity of zeros; other than the forms that trail in something else. Every real number has infinite precision. This is the mathematicians perfect continuum. Working on that continuum we find practically that to achieve say 1.001 inches is very good precision in metals. Then again to get to the next level:
> https://www.youtube.com/watch?v=sFrVdoOhu1Q
> and of course the mathematicians have already gone beyond all of this in their form, right?
>
> So ultimately though they may go 'mum here, they have legitimated the infinite forms, limited as they may be, long ago when they formed a notational convention that goes in direct conflict with physical reality.
>
> >
> > To argue that the value of the digits are infinitessimal in the 1/3 instance does nothing to the informational representation. Likewise epsilon/delta will suffice just as it does for the irrational values as Dedekind presented it. The fact that the digits are redundant is handy. Still better if we went to modulo three representation one third would simply be 0.1 and so no puzzle even ensues.
> >
> > For those who like infinity I would think they'd like to let in this infinite value representation of a natural value.
> >
> > For those of us who do not like this form we should then reject it as well back on the accepted repeating decimal result of the 1/3 computation. The augmentation of the radix point to the natural value exposes a special representation that is not taken seriously by mathematics so long as it is regarded as the rational value all over again. It is not. The division operation has been removed. A new unit value has been achieved.
> >
> > As we approach this play on unity with fresh eyes we could even push it farther so that a new unit position of say 123 is enforced. Of course what we will have is the concept of the rational value, except no division is necessary. Now we have a counting form of the rational value. This is apt I think. Addition is far more fundamental than division. Also though this concept of unity as bridging to the concept of unification through unitization raises the lid on an otherwise closed down and done thought process. At the bottom of it all is the modulo number. the 123 as a unit instance is nearby to a reradix, sir.
> >
> > These issues of course bleed onto the continuum and what we mean by it. What we even mean by countable can be broken down but for the mathematician's pure form of it in the natural value. Here now I come to wonder if even that form is undeserving of its name. Rather than 'natural' these ought to have been called 'perfect' or some such, 'exact' perhaps. 'Discrete' is pretty good though a bit more generic. Nature is far more tricky than the natural number. Reality versus the real number; well; you'll need three of them at least. Is each one then a third of reality? I do mean to belittle the terminology because deference to the past assumptions is likely partially to blame for the bottleneck that we are facing. As you bow to the masters who came before in a long chain of masters who bow to their masters your own mastery is suspect I believe. To cover the ground in a new way could be instructive particularly if we arrive at some new options.
> >
> > Under the structured approach, as we legitimate the radix point as a data structure, sign comes next. There I already have productive results. Here I cannot say yet. There is movement at least in terms of interpretation, and the fact that interpreting the unit could hold this far is encouraging. The rational value as broken has been established already. That I've come around to a new form of it through the unit interpretation feels pretty good. Best of all we are back to incremental counting and modulo principles. Exactly how polysign took off. Exactly how digits work. Spacetime is structured. Whose job it is to get it from thin air: will physics ensue directly? Should our concept of number get us here? Wouldn't this actually be the real number? Has mathematics taken itself hostage through its nomenclature? What an accumulation has occurred, and for those who manage to map it all like the lines of a bible; well; have they really done themselves any favors? When does simplicity cut in? Where does complicity leave you? I so must insist that I am not complicit with the actions of my government. To see through the eyes of a juror who bought Russiagate and in the midst of near nuclear war should a few mistakes happen... Sussman is off by propaganda alone. Triple down...

we see once again you do not know how numbers work

[Ross A. Finlayson]

Yeah, there's nothing here but foundationalist rhetoric and fundamental basics.


In set theory a "model" of some numbers, is a set, that, according to how it has
fundamentally defined the model's definition of relation, for theories other
than set theory the objects of the theory.

Then natural integers are usually the simplest model, with a beginning and
then ending with infinity. A usually simple model is a beginning and end,
and infinity in the middle, modeled just like a set of positive and negative
integers, i.e., usually alternating. This is where usually "the very least definition
of set that can be built upon with its relations a model of numbers", here is
showing that natural numbers is ordinals and simple, and both signed integers
and also from the beginning and end or "0" and "infinity" with "unbounded",
the about same relation that makes for alternating the expansion of bounds
for the signed positive and negative, works out about as well for the finite
and infinite.

So, then people call something like the set of numbers a "model" of numbers
for arithmetic, but that's not free, here it's only so free as "this model of
natural integers basically implements successor for induction and rest is
built on that", after modularity or that the difference between successive
integers is always the same, or "integer's first constancy axiom".

(Instead of for example "model of signed as groups of all the unsigned".)

Then rationals after "usually some signed integers however defined here"
then "the equivalency classes of all their ratios according to modular reduction,
or cancellation of common factors". Different set these models: 2 =/= 2.0
according to "set intensionality", but "set extensionality" has that there is a
defined relation: "the _value_ of 2 is the same as 2.0 according to that 2.0
as a faction has reduced form denominator 1 so it has an integer value".
Then every other rational is defined having an integer part and a non-integer
part as about as simply.

Then, each real number is any convergent, for example constant, sequence
of sums of rationals that make series, called Cauchy, then the reals are usually
"the equivalency classes of Cauchy sequences their values as they have the
same limit". Again, 2 =/-= 2/1 =/= 2.000..., the sets, while according to values
there's of course that 2 = 2/1 = 2.000... in "set theory" after making "model theory"
of it that there is assignation of real-valued values that according to interval
arithmetic, are well-defined.

Formally _there's not much more_ for model theory defining this kind of
example of "standard Archimedean real numbers, their values, in set theory,
for example ZF, with integer constancy, rational reduction, least upper bound,
and measure 1.0, according to model theory".


In set theory everything's a set - ....

For some people "pure set theory" is "definition and closure of set-theoretic
operations according to membership like union, intersection, and disjoint,
modeling closed syllogism, on whatever other objects are so defined",
there's also that "pure set theory" is "only set theory". Then it's like
"all the way down in the axioms there are none and these numbers
are all the sets, and vice versa".

Set-builder notation is concise for closure, "N", "Z", "Q", "R". Here for
example "Z for Zahlen the signed integers, though Galois automatically
defines it a group, for that matter Q and R fields, after inverses,
according to set builder quantification or "elt" these are all only by
"values of their models".

(That "the models of groups and algebras happen also to be models of
modular rings and magma", is only after a roundabout way of basically
encapsulating all their set access to values, extensionally must usually
in the extreme, standard 'continuous' real values.)

A lot the point is "topology and number theory quite totally agree
all the interpretation these models of numbers all in pure set theory".

[Timothy Golden]

Is this Zahlen note to distinguish it from the Russkies?
I do appreciate your thoughts here, Ross.
If you had a formula that wound up doubling x like:
y = x + x = 2x
it's not as if that two has the possibility of becoming 2.3 is it?
Yet it really is this concept of unspecified digits being unknown that I am going to jell on.
It is the sensible treatment of the irrational values applied onto the rational values that gets us back to coherence!
By this I mean that as we march along filling out the digits (which were unknown prior to our work)
we secure a superior value to that which came before. To the physicist they've already pushed to their limits and if they have to go out of their way to secure a few more digits that choice will have to be weighed against the time it will take, the cost of the materials and labor, and the possibility of other superior solutions. As to who is engaged in reality... definitely the physicist is wearing that hat. The mathematician's hat may accordion fold out to obnoxious lengths; it may have multiple fake flowers that squirt mysterious substances; but in its compacted form it tries to look serious and hold up to the physicist's and the engineer's versions.

The geometer will appreciate such limits in his work and probably at times work tirelessly to avoid mistakes which produce mistakes as byproducts.
I cannot declare mathematics to be a mistake, yet I can expose some mistaken forms. Is it the case now that physics and engineering should claim their own version of the real number rather than tuck themselves in with the mathematicians? Which way then will the philosophers go? Are we discussing a quantized two versus a continuous two and is the physicist even aware that these are purely mathematical forms? Or are they physical forms as well? Hah. Now we are treating this as a freshly opened can. As to what else might be in there... I'm hoping we don't pull out a rat's tail at the end. Until then it's a tasty treat on usenet.

> defines it a group, for that matter Q and R fields, after inverses,
> according to set builder quantification or "elt" these are all only by
> "values of their models".

The R model is getting antiquated. The Q model too.
What is digit chasing but epsilon/delta theory?
A mathematician slams his foot down on the floor and says shrewdly: "That's only for the irrationals, Tim, The real numbers are perfect other than the irrationals. You pick a value and there it is on the line." "And when when you pick the value 1.234, sir, how secure are you in that value's position on your line?", said Tim, "It's just not that easy. You see?" Well then was it merely a matter of the maker of the line making the mark and labeling it or would it be wiser to presume the line came premade?

Plenty do, and they tend to be the ones that are followed, as in when a carpenter pulls out his ten foot tape measure from his pocket and jots down a few notes on a piece of paper; the tape running in and out, in and out, springing back, sometimes quite quickly and other times not so quickly. Still, the tape is treated with care. Even the thickness of the hook on the end is accounted for, the ovaled holes being exactly its thickness beyond the pins; give or take. The mathematician, at the hardware store ,comments to the store manager: "All these tapes are manufactured badly. You see the play on the hook at the end?", to which the manager snickers, and says: "Brilliant observation, sir. I'll be sure to pass that along." The mathematician walks out of the store proudly, thinking to himself about the dimwitted dysfunctional systems in the factories, feeling grateful of his ability to stay above the fray. The store manager watches him and thinks, "If being off by one never felt so good then being stuck at two never felt better, eh?"

If the numbers that behold physical reality are not the real numbers then should we insist on a new terminology for reality or for the real number?
Or should we expect humans a hundred years from now to be still using such slanderous language and fully adapted into it without even knowing it?
This unfortunately is the status of mimicry whereby the present generation happily insists upon particle/wave duality, for instance.
This real problem has been going on for quite a bit longer.
Is it possible that real analysis is in fact an act of bigotry?
Or would that be reverse bigotry?
Or am I the bigot?
Really, I'll leave that one on the table here for somebody to slam me down.
Oh, and there is as some dismissively call it: merely notation.

[Ross A. Finlayson]

A lot of times after roots and the algebraic,
and the elementary functions,
there's "write numbers in continued fractions,
also with their interesting properties they're algebraic",
I suppose they write operations, in a form which can be
construed "rational roots", continued fractions, also for
":the continued fractions in example that find their roots".

Already with integer-part/non-integer part real value, back
and forth from R and Q as what set theory holds it,
there is of course besides what holds it what contrived also holds it,
"these least contrived R and Q are part of theorems that
according to descriptive set theory and for example topology,
it's not so much they exist the sets as form the theorems,
models in model theory". (Fundamental models in model theory.)

Then also Tim these numbers you describe are like "under
symmetrical differences, roots for example fall about various
inversions of projections of roots". Then it's about what is written
and how it's written their value, that the descriptive theorems
define the value according to their symbols.

Then the symbols like "equals" and so on, "relates", here
there are basically keyboard symbols and concatenations,
written in "as if writing math mode TeX for AMS style",
that the caret or ^ is for exponentiation, while, underscore _ is for subscript.

Then for example there are Stirling cycle and subset numbers
under combinatorics, that Knuth gave bracket notations.

The integral is the stylized Summation after Sigma,
where Pi is product, derivative written 'd' and limit: "lim".

Functions are usually written their abbreviation,
with variables from the keyboard alphabet.

So, there's basially "as you write them" and "what it means" and, "when".
(Or "where", ..., "theory of only one question word".)

For "new numbers" is whatever objects, models, their values
in their language or space of values, they have values that relate,
to other numbers, their values in their language of space or values.

Here "language" and "space of values" are separate not so much
they differ as utterances, words, are in the language of values, while
the measure, ..., is in values, there are standardly both models.

Then pretty much "limits are in the language, values are in the space".

[mitchr...@gmail.com]

.333 repeating with a remainder of 4 is still a valid quantity...

[Timothy Golden]

Well your thoughts are divergent; I would not say incoherent, however,
the difference between 2 and 2.000...
leaves Tolstoy in the dust.
Were I ever to claim that the difference between these two representations was flatly and unequivocally zero, as in naught; niet...
it would be like serving Poutine on July 4th.
Getting your cultures crossed up; which is which, and to which which was discrete, and which was continuous, would be only a small portion of the discussion to be had when differential whichness never even allowed for how we got there! It's like you just snapped your fingers, and voila. Sorry pal, it just doesn't work this way. You've got to work your way down to all of those zeros and in the meantime which which was along the way was more than those two ever got you. I wouldn't even care to guarantee that it was actually that which you thought, and if not then which was the last? And wouldn't the error be of interest? Perhaps the answer lies in
0.14159276...
I mean, at least you've got the three in your hands this way. What would I find along this corridor? Perhaps I'll try it and see. Here lays the corridor of pi minus three. If I treat it as special will it become so? From an axiomatic vantage the answer is yes. Certainly. Proceed, sir. I apologize that some of my graphing has been missing its meaning. Pretty colors sure are nice, but we've got to get down and dirty soon. Real Soon. Like before the fission fire hits us in the face.

Biden finally agrees to play Russian Roullette...
"They had me buzzing so hard on something; I don't know what it was, but man, I mean, c'mon, man, you just don't do that to your president." Poor old haggard covid cancered sinuses aten out by cocaine Joe slips behind the curtain for another treatment, comes out in just ten seconds, lively as can be, and says: "You know I've been having some funny dreams lately. It's like voices are talking to me from outside my head." And You say, "Go on, Joe. I'm all ears.", tired of listening to his babble.

[Chris M. Thomasson]

2 - 2.000... = 0 right? ;^)

[Ross A. Finlayson]

Or for example "2 - 2.000... = 0.000...".

Making three notations 2, 2/1 or 2/0, and, 2.000...,
for example makes "kind of like significant digits means
123.0 + .01 = 123.0 and 41 * 59 is like 2400, makes
for where integers are perfect constants and rationals
are down and reals are in significant digits".

Here "perfect constants" means "infinite precision",
in scientific computing there is mostly significant digits
and exponents.

In machines there's words and extended precision algorithm
and interval arithmetic, for example.

"Muldiv", ..., muldiv is pretty great.

For something like "2 --2 = 0, but 2.0 - 2 = 0.0 and 2 - 2.0 = 0.0".

For when "these examples in notation should also be examples in terms".

When I learned about sighnificant digits I was like "this is great, no longer have to
remember more digits than the most of the inputs", besides that
according to approximation theory, also "products in scientific
notation truncate and implement roundiong".

Of course it's expected that "perfect constants are multiplied all the way through,
only then truncating the scientific product".

It's like I expect everybody to have a modern 20'th century science education.

[Ross A. Finlayson]

Oh, I'm with you - according to approximation theory these intersections
"make some grid", about "the least significant differences in these products,
are because the inputs are so right and close to each other, implementing
some kind of arithmetic coding".

(That
"products in the module
fall in the module
and preserve precision.")

[Chris M. Thomasson]

On 7/29/2022 6:26 PM, Ross A. Finlayson wrote:
> On Friday, July 29, 2022 at 12:41:24 PM UTC-7, Chris M. Thomasson wrote:
>> On 7/29/2022 12:15 PM, Timothy Golden wrote:

[...]

>>> Well your thoughts are divergent; I would not say incoherent, however,
>>> the difference between 2 and 2.000...
>> 2 - 2.000... = 0 right? ;^)
>
>
> Or for example "2 - 2.000... = 0.000...".

Okay. So:

2.00 + 2.000 = 4.00000?

;^)

[...]

[Timothy Golden]

By the laws of precision I'm pretty sure the result is 4.00
It would also be true that:
2.00 + 2.001 = 4.00
These 'real' numbers are much more realistic than what the mathematician uses.
Of course if they don't apply to anything then they are not real at all, so let's say marks on a stick is what we are talking about, in inches.
This is the way the physical world works computationally and this is that world in its most serious form.
We cannot do any better and we admit it carefully. Some more carefully than I am doing here, as when physics announces a new constant as:
8.8541878128(13)×10−12
but I was never using this form. We always just did that last digit thing where a five or up rounds up at the end of a computation to the conserved digits.
This was just a 'number of digits' type of precision, and I suppose it can get more complicated.

I think it is wise that you threw up the 2/1 form of two, and there are more there in the rationals, and mathematicians, on usenet anyways, do care to treat those twos as unique since 4/2 is different couple of integers than were 2/1. This is of course just one more falsification of the rational value. Simplicity and organization slipped at the doorstep with the rational footing. And that's not even attacking their divisive nature. To step cleanly is what we seek, and as we do get on a staircase regularly in mathematics it is usually by preserving the radix of computation that some reasonable results accrue. This just is not so for the rational thinker, and in that those are compromised then so is the real value compromised, and in that the decimal values that the engineer uses are not the real values, then the distance between the camps grows over time. Well, this is some keen rhetoric, and if you want a straight staircase you had better head back for the natural number of mathematics, and lo and behold there it is merely with a little dot added to its form:
2.00 <-> { 200 , 2 };
and in computation these are literally operative values. In hardware this might require barrel shifters and all sorts of complexity to do the job efficiently... especially multiplication. Meanwhile the group theorist plops down the product and the sum side by side and there is hardly any difference between them, as if to declare: "Here are you pure operators." I do or did like this approach. Polysign numbers fit in with it famously. Pick a z1. Pick a z2. Take their sum. Take their product. It's all good and straight-forward once you realize the balance. Yet like the value two, the product can take on more interpretations than this. We'd actually like a dimensional gain product. Ah... is this the route to take? I can't say that I've ever put it quite like that. Of course the Cartesian goes straight into its boxy form. Whence does polysign go? Best of all we have a P1 product that does not gain in dimension, yet still does some math. The P2 version seems a bifurcation of a sort, or at least it could. Yet how one would apply the P2 onto say a P3... is relativity involved? Wow. I could be meandering into something big here. Of course it could as well be an apparition. Still, when we multiply we do tend to get rather more than we started out with, which is why it is called the product; it is very productive. In contrast to the sum, which merely yields what you started with into a unified form. Well, that is something to be respected too, but not so much that you shouldn't work variations. I do see somehow in an abstract way that as a P2 meets a P3 they must do so on some sort of playing field. So far the only playing field we have is the tatrix, but that isolates them into their own ranks. Well then, should it be that a grand tatrix product will yield so many things?...
T1 T2 -> P11P12@P11P22.. @ P21P12@P21P22.. @ P31P12@P31P22.. ...
Here my double dot notational ellipsis is in use and gets the expression down to one line. Expand out to three dots if that makes you feel better.
It looks like we will be casting both ways in the general tatrix product. That does seem balanced:
T1 T2 = T3 = P1 @ P2 @ P3 ...
and I do believe that is my first usage of the mixed form. They are self organizing at this level of notation. It wouldn't be wrong to call these 'interdimensional products' or some such and the whole family is laid out to see within the tatrix notation. In the ordered form I suppose no conflict will arise and we would nearly say goodbye to all those obnoxious signs that you all have refused to get used to. (a,b) is a P2 form. (a,b,c) is a P3 form. (1,0,0) is MU in P3. That would be MU first notation. It's the rotor that makes these things happen. All good churns have blades. These churns have n blades per churn and the tatrix has n churns.

I'm not fond of the complexity that I am introducing here. I'd rather keep things simple. Still, the option at least to introduce a relative reference frame betwixt say a P2 and a P3 seems obvious. They are foreigners to each other. They do not generally interoperate. The rule of explicitly stating what Pn you are working in and staying in it are gone here in this grand product. Yes, there is a simple cast but is there more than just that simple cast? I think so. Yet if we grant every Pab a unique frame to every Pcd then that seems like quite a bit of data. It just has to be said as well that emergent spacetime form is T. Whether it is T3 or T4 or so I don't really know. I just know that there is arithmetic correspondence.

Sorry to dump that here.
For now.

>
> ;^)
>
> [...]

[Ross A. Finlayson]

Implementing addition with muldiv, ....

Because 2+2 and 2 x 2 are same, makes
sense if they are different that the product
and sum are same, or here that they're linearly separable,
happening also to equate halves from the product,
besides the sum that is always halves.

But, that's higher order in the linear product operators,
while also the positional notation and length notation,
here accumulate.

This is where products in measurements is besides
perfect constants and their definition of linear systems,
all science is in scientific notation for values and sufficient
values for the constants, what result their respresentation,
for example "pi is as long as the sum of these exponents,
values according to their products in numerical value".

Then science and all quantum mechanics is these are
measurements, the real perfect value that they
have the systems are what these measurements
in these systems of equations attain to.

Then, a goal of approximation theory is for example
closest to that, or for example some best-value.

[Ross A. Finlayson]

There is scattering in quantum theory quantum electrodynamics,
then for tunneling in quantum theory chromodynamics, which are
hadronic and leptonic, ..., just pointing out that the field, is that
scattering and tunneling are basically _opposite_ theories, to put
together, in an interchangeable theory, or sufficient to terms.

Then there is screw theory, you mention a tatrix and define a propeller,
screw, keeping in mind that screw theory is that any periodic action,
only results a (linear) regular time action, propelling what is the action.

So, you mention blade churn and it's what to attach, to what you can
find that all the "great majesty of mathematics" has here two then three
simple theories that address the same objects, what aggravates and reconciles,
for example then directly to fluid dynamics - whatever wave mechanics you like.

Then there is combinatorics, figuring to "find the combinatoric expressions,
then what result under formulas simply their classes in combinatorics",
besides of course "and also here's a counting argument for application".

Then continuous/discrete and wave/particle are basically the mental
concepts, what suffice for reason and science "real".

[mitchr...@gmail.com]

The difference of .999 repeating and the first integer
is one divided by infinity...

[Ross A. Finlayson]

On Saturday, July 30, 2022 at 10:56:15 AM UTC-7, mitchr...@gmail.com wrote:
> The difference of .999 repeating and the first integer
> is one divided by infinity...

Sure, 1/oo = zero.

[Archimedes Plutonium]

On Wednesday, June 1, 2022 at 9:47:12 AM UTC-5, timba...@gmail.com wrote:
> Is 0.333... a valid number?

Tim, you need to reference something like 333....34 to AP's work of infinite integers, from 1993 to about 2012. I had many discussions with Karl Heuer, Alexander Abian on Infinite Integers. In 2012, when talking with Dik Winters and Chris of Univ Arizonia, or thereabouts I no longer had need of infinite integers for the Decimal Grid System becomes the true numbers of mathematics. The Reals are mindless b.s.

It is always good to cite references to others who worked on the subject, before you.

[Timothy Golden]

Well thanks for the links AP. No, really, I would review something if you have a link. It does seem like an obvious format so it wouldn't surprise me if somebody else did try it. Truth is I did arrive there by the analysis of the decimal point, and it was a slow process, which proves at least what a creature of habit I am. I'm a bit more keen on the ambiguities of these choices rather than latching onto this as some great proof of infinity. To what degree is inductive reasoning a step away from direct and simple reasoning? Should it be treated as a weaker form? I think that to accept the inductive infinite value 333...34, and the computations that can be done with such values, that we have stepped into a region of mathematics that is severed from the finite forms. The finite forms are good enough, and we struggle to achieve even twelve places of precision in physical reality. What does the addition of one onto 333...33 mean? In essence I think it means that these numbers have a head and a tail: that our numbers are two-sided somehow. That our language is two-sided somehow. This means of notation that we are so heavily engaged in is two-sided somehow.

I wonder to what degree is the auditory form of learning the mimics' scandal? As babies we imitate those around us and our native tongue gets developed. All future translations stem from this early auditory form. Radio and television: the picture worth a thousand words is not actually a truthful statement, when ten words can build a picture for a generation of humans to live by. The avid reader versus the avid listener: is there a difference? The clean sound of NPR: I grew up with it as a kid. Listened all my life until their lies caught up with them. Steering the conversation: or the denial of such steerage: as we have matured as a civillization beyond national boundaries; as we have engaged in a global human identity; these poor nationalist sources have sold their souls to their nationalist leaders. I must ask: what is the difference between nationalism and naziism? Is it merely a matter of how far you will go for the state? How far have you gone? How far have they gone? Would you care to take it any farther? Is your country superior? Do you pledge allegiance to a flag? If they've got a gun pointed to your head I do recommend the pledge, but other than that it should not be done except in the name of the planetary identity. We are Earthlings. Corporatism has no fit to this global identity. It is strictly a matter of species. Certainly there is more, but as to the nature of the island that we all stand on there is no conflict in this identity. It is obvious. It is a matter of natural law and the accumulated knowledge of people who once upon a time did have an edge to their map, and beyond that edge laid the unknown. Whatever systems of power brokering go on and as they implement means to control the population of Earthlings the pitting of one pool of Earthlings against another, particularly via a long series of lies such as NPR has committed, is totally unacceptable.

They do in fact have clean auditory quality, and somehow have built a reputation as an intellectual source, yet when that intellectualism is compromised what exactly do you call it? When they cannot have the conversation and when they throw the person that would like to have that conversation under the bus, albeit through some plan cooked up by operatives elsewhere; well to say that the system is rigged is one thing. To realize that the auditory channel is a special mechanism is another. As it pours in through our ear canals where does it all go? Consciousness has little to say about it. There would have been a time prior to technology when one man was listened to by many and at that time what one broadcast as such a leader would develop a first form of rhetoric. Taking this global as can now be done is a problem of a multilingual nature. So it seems that the mark of civillization to achieve a first global tongue was an accurate assessment. At least knowing that such a thing exists helps quell my enmity. https://en.wikipedia.org/wiki/Esperanto

[Archimedes Plutonium]

On Sunday, July 31, 2022 at 9:24:17 AM UTC-5, timba...@gmail.com wrote:
> Well thanks for the links AP. No, really, I would review something if you have a link. It does seem like an obvious format so it wouldn't surprise me if somebody else did try it. Truth is I did arrive there by the analysis of the decimal point, and it was a slow process, which proves at least what a creature of habit I am.

Throughout the years 1993 to about 2012, I was posting in sci.math under the title "Correcting Math". Thousands upon thousands of posts and in discussion with Karl Heuer, Alexander Abian,Dik Winters, Chris Heckman on what I called Infinite Integers, mixed in with p-adics. What I was attempting to do is find the real true numbers of mathematics with a well defined finite and infinite.

That well defining came around 2012, when I finally realized a "borderline" well defines finite and infinite. You cannot talk about finite versus infinite unless you have a concept of a borderline between them. Reals, complex of Old Math are phony, even Rationals of Old Math are phony, not to mention irrationals. Old Math numbers are all phony b.s. for they had no borderlines in their number systems.

Once I found the key to well defining-- borderline, then I needed to find the actual border of infinite with finite-- Huygens tractrix-- 1*10^604 and its inverse. This then causes the true numbers of mathematics are Decimal Grid Numbers. We throw out Reals, Complex, Rationals, Irrationals. The only thing left standing is Decimal Grid Numbers.

So from 1993 to 2012, I was playing with these infinite strings of digits such as 333...34 or 0.333....34 until 2012 in a discussion with Dik Winters and Chris Heckman (Arizonia or Arizonia State Univ.), the lights came on for me-- BORDERLINE is the key concept that straightens out the mess of Old Math numbers.

So, I would appreciate it Tim if you referenced my work and the many listed persons in colloboration with my work of 1993-2012, when you bandy about numbers such as 333....34 for they are not numbers of mathematics at all. But they are a stepping stone in well defining what true numbers of mathematics are. They are a stepping stone of telling the person who has a logical mind-- try a borderline, and then see where the borderline is. Finally see what the true numbers of mathematics are --- Decimal Grid Numbers.

Correction of Math was compiled by me and published into a book, available on Amazon Kindle, which richly discusses infinite integers, borderlines.

Correcting Math// Math focus series, book 1
by Archimedes Plutonium (Author) (Amazon Kindle edition)
--- quoting ---
Cantor was so horrible, so ignorant of defining finite and infinite, that you could hand him any number in the world, and Cantor could never tell you if that number was finite or if it was infinite. That is how awful was Cantor's notion of the infinite as "endless". With such a meaningless definition of infinite as endless, hand Cantor any number-- never is there a infinite number. All is finite with a pathetic notion of "endlessness". Yet to Cantor-- give him 0.33333.... or 0.9999.... and he says it is a finite number even though it has endless digits of 3s or 9s. Does that sound like a mathematician or logician to you with precision in mind? Or to a German of 1874 who will enter an insane asylum?
--- end quoting ---

And also, a friend of mine wrote a Wikipedia page listing Infinite Integers. That page is found on Archimedes Plutonium - EverybodyWiki Bios & Wiki Infinite Integers "Plutonium's philosophical view includes objects which have a decimal expansion which never ends,..."

I no longer use nor need infinite integers. They were a bridge, a stepping stone to reach the true numbers of mathematics-- Decimal Grid Numbers.

AP

[mitchr...@gmail.com]

.333 repeating with a remainder of 4

What invalidates it?

Mitchell Raemsch

[zelos...@gmail.com]

2=2.000..., no difference

[Timothy Golden]

Well for the Cartesianers their minus sign can only reverse. In polysign we get rotation.
In truth that reversal is rotation but it is constrained to one dimension; P2. Up in P3 we have the complex plane, the resultant of a modulo three form of sign.
As well we have the underling P1 to consider, and to what degree are compositions or decompositions done by it rather than by P2? than by P3 even?
This is somewhat the interdimensional problem. There are lots of ways around. Important to all of them is simply realizing that MU was the only sign needed to construct them. The plus sign is MUMU. The star sign is MUMUMU. The sharp sign is MUMUMUMU. The minus sign is MU. The zero sign is NU, and in P3 takes MUMUMU as its modulo form. This works out in P2 as well, so though the zero sign is needed technically it can be done without just as the Cartesianers have done without it.
Notationally the inverse obviously no longer uses the minus sign. That is only the inverse in P2. In P3 -z+z is the inverse. In P4 -z+z*z is the inverse.
There is no axiomatic requirement of an inverse in the polysign construction. It just shows up as a side-effect of the law of balance. This law of balance is lacking for the Cartesianers. Where is it in axiomatic form? Where do your (x,0) and (0,y) interact? They do not interact! It is only by convention of placing them manually in a pre-agreed way that you get the same results as the next person. These angles are already demanded by polysign out of the gate. It is this comparison which allows me to pry at the joinery of your box, sir.

That this layer of confusion would happen to occur in conjunction with another layer of confusion I find completely believable. Stop bowing to the masters and start challenging their claims. What sort of people would insist on such? Could it be that they are the straight A's? The perfect mimics? The teachers' pets? Oh yes, stroking egos is a big part of the job: "Good boy Johnny. You got your number up through a hundred already. Who's your daddy?" Johnny looks up at his father; barely five it's quite an angle, and imprinting hard he says: "YOU ARE Daddy!". The father grins a grin that could not get any grinnier, thinking to himself, "What am I gonna do with this kid? He's got me beat by five years already."

If after twenty or so years of such training you are finding it hard to break your way out of the box that you've built yourself and you find yourself merely tacking up braces in the corners over and over again, recovering the walls and the ceiling and the floor, as it grows darker and darker in your box, you wonder to yourself: "Is this all that there is?" And it comes back to you... "Good boy...", and you go back to tacking up strips a new way.

>
> Then there is combinatorics, figuring to "find the combinatoric expressions,
> then what result under formulas simply their classes in combinatorics",
> besides of course "and also here's a counting argument for application".
>
> Then continuous/discrete and wave/particle are basically the mental
> concepts, what suffice for reason and science "real".

Well, I think it suffices to say that I don't have all the answers, but that we are engaged in a progression, and that to cast these problems as open at this point to superior future constructions; particularly of a theoretical nature that is more independent of empirical means; is entirely valid for at least one strand of the processing power. This 'branch', so to speak, will satisfy the concept of unification by denying the separation of philosophy from mathematics and physics. As such this discussion on number that we are having does in fact mean something. It is a place of clean divorce, where the engineer means one thing, and the mathematician another, in the same damn number!
1.23

[Timothy Golden]

Well I do think our interpretations are unique but that the ground we cover is similar. I think ultimately we should all chalk ourselves up a tick for working in the open here.
The structure which journals provide and their system of approval is that of a dog trainer more than of a humane and open-minded, uncensored, free flowing, say what you want when you want, kind of place. The idea that people who publish to such places are free thinkers is a claim worth investigating. So we have to go to book form to find that. fine; good; but here is the wildest form of all. AP, I would not be proud of posting so many posts to usenet; especially not if you've swamped your own claims. Especially not if you've attempted to cover over other people's works here. It really would not surprise me if there are agents of several regimes prepared to step in and spoil usenet completely. How many uncensored environments are there? I can tell you this: every one that is censored that I've tried to post to has neg'd me. That includes the censored usenet. I feel so grateful to have sci.math as a resource. I am ashamed of those who shit upon its deck, and while to some I may appear as one of these, I do try to vary my content and build my writing skills as I go.

Of course there are special situations with special people, such as yourself perhaps, which expose what journals ought to have allowed. Especially in the digital age there is room for all to be on record. There can be no doubt about that. In Petabytes We Trust. Your persistence, AP, is above and beyond my own. I am relatively lazy I suppose. Still I did just do a search for your: https://groups.google.com/search?q=%22Decimal%20Grid%20Numbers%22
but it has just three entries, though two of them are going back to July 31, which I see was just yesterday, today being August 1, 2022. I think that you care to own these numbers as your own stands as credit to these numbers themselves in their free-standing form without any human interactions. That they rest upon an inductive call is rather important I think. That they can be defended via prior use through structured analysis is as well quite relevant. That some of this analysis does in fact involve rejecting the rational value as fundamental strikes at the heart of mathematics, yet there is still a pulse. One clean cut and a pull and the thing appears ready to heal and go on, no? That such an action is a simplification that actually falls into line with modern computation could be cause enough for the old real analysts to strike off for their own rational processors to save the day. Branch Not Equals never worked so good!

[Timothy Golden]

I think what's new is that you can have an infinite value ending with a specific digit.
It's like arguing about inifinite evens and odds. Whatever infinite value you have it will have to be odd or even won't it?
These are the digits you can choose from: 1234567890.
And hurray, QWERTY got it right!
Our numbers have whirling, clicking, and popping sounds if you listen carefully.
Still, the inductive forms of infinity are encumbered.
Then again at their tail such freedoms arise as exist with the ordinary natural value.
If you start getting complicated at the head or the tail your work is cut out for you when it comes time to get a product, but it appears it can be done.
For those puritans who deny infinity theyhave to lay the inductive step to waste, and what then wastes away with it? What are the other consequences? Repetition gets so repetitious that I grow bored. If you bore first then split out your boards you get perfection, more or less. It helps to have a sharp auger, too. File work comes first.
One, Two, Three, and then you are done. How's that?

[Chris M. Thomasson]

Rotation occurs in the roots of complex numbers as well. For instance
simply negating a 2-ary root of a complex number z gets a rotation by
PI, which is the other root. N-ary roots are fun.

[michael Rodriguez]

In one considers just a collection of n digits, n is prime, we have
sum and multiplication, what will happen if we endow the collection with the
usual metric, but also a p-adic metric simultaneously (distances,proximity)
One can executes this or that rounding, but is it possible to mix em,combine them ?
;0

[mitchr...@gmail.com]

There is math before man's mind. We discover it.
It is real. It is not our artificial invention.

Mitchell Raemsch

[Chris M. Thomasson]

On 8/5/2022 6:36 PM, mitchr...@gmail.com wrote:
> On Friday, August 5, 2022 at 3:13:42 PM UTC-7, michael Rodriguez wrote:
>> In one considers just a collection of n digits, n is prime, we have
>> sum and multiplication, what will happen if we endow the collection with the
>> usual metric, but also a p-adic metric simultaneously (distances,proximity)
>> One can executes this or that rounding, but is it possible to mix em,combine them ?
>> ;0
>
> There is math before man's mind. We discover it.

Exactly. Well, imvho, there was math (had to be) before "Mans" mind
indeed. See, imho, Man is not the only intelligent being residing
withing our universe. Right? Math is math, and just might be
"universal", so to speak. ;^) Different versions of the same base truths
in math. A vast diversity of 2+2=4. What about 1+3=4? Ahh, the infinite
ways to examine math. Although a scale has to balance on many planets
out there. So, math was born from a balanced scale? Humm... Too deeeeep.
;^) lol.

[mitchr...@gmail.com]

On Saturday, August 6, 2022 at 12:46:41 PM UTC-7, Chris M. Thomasson wrote:
> On 8/5/2022 6:36 PM, mitchr...@gmail.com wrote:
> > On Friday, August 5, 2022 at 3:13:42 PM UTC-7, michael Rodriguez wrote:
> >> In one considers just a collection of n digits, n is prime, we have
> >> sum and multiplication, what will happen if we endow the collection with the
> >> usual metric, but also a p-adic metric simultaneously (distances,proximity)
> >> One can executes this or that rounding, but is it possible to mix em,combine them ?
> >> ;0
> >
> > There is math before man's mind. We discover it.

Hawking said "We shall know the Mind of God."
He was right. But he was a hypocrite in the future.

> Exactly. Well, imvho, there was math (had to be) before "Mans" mind
> indeed. See, imho, Man is not the only intelligent being residing
> withing our universe. Right? Math is math, and just might be
> "universal", so to speak. ;^) Different versions of the same base truths
> in math. A vast diversity of 2+2=4. What about 1+3=4? Ahh, the infinite
> ways to examine math. Although a scale has to balance on many planets
> out there. So, math was born from a balanced scale? Humm... Too deeeeep.
> ;^) lol.
> > It is real. It is not our artificial invention.
> >

There a Mathematical God for physical math before man
back to the BB's math.

Mitchell Raemsch

[Archimedes Plutonium]

Still, the Timothy Golden nutjob steals the math work of AP, and tries to cover it up in b.s.

On Saturday, August 6, 2022 at 3:53:22 PM UTC-5, Archimedes Plutonium wrote:
> William J. Burns why is Kibo Parry M play acting Banerjee and spamming sci.physics, up and down the board. No wonder all dot edu address posters fleed science newsgroups by 1996 with the CIA spamming science day and night. Nothing but CIA spam left and right, CIA spam mocking and deriding and stalking posters. No dot edu poster can stomach that kind of b.s. And yet, here in 2022, we still have the stalking mockery of CIA Kibo Parry Moron
> >
> > On Saturday, August 6, 2022 at 1:18:49 PM UTC-5, Michael Moroney wrote:
> > >"bozo"
> > > fails at math and science:
> > >"barking fuckdog"
> >
> >
> > On Sunday, April 3, 2022 at 8:15:42 PM UTC-5, banerjee...@gmail.com wrote:
> > > On Monday, 4 April 2022 at 10:15:49 UTC+10, plutonium....@gmail.com wrote:
> > > > So, we see that Arindam Banerjee is a Russian sockpuppet in the newsgroups. Something I suspected 5 years ago, but only made clear with the Russian invasion of Ukraine. Explains why the AB posts date time marks are off from being in Australia or being in India. Explains why he cannot delete his posts. Explains why his tom-foolery in physics is just a cover, to spread his political b.s. babble.
> > > Not so, stupid Archie. I certainly am indebted to the Russians (Soviets) as I was brought up among them in the commune my father managed, back in the sixties. Thanks to them I had a totally marvelous, enjoyable, happy childhood which made me what I am, the greatest genius of all time and sole god among lotsa devils. Of course, the Soviet experience was bolstered by Catholic - Jesuit influences; the sylvan charm of the native cultures of the lovely Indian state of Jharkhand; and my own Puranic-Vedic-Upanishadic tradition that is loosely called Hinduism. So you see, o stupid and ignorant Archie, that I am an invincible alloy, not a Russian sockpuppet. My details are clear and free in my facebook timeline, where I have hundreds of friends, mostly strangers who asked for my friendship. They all like my posts there.
> >
> > More CIA & FBI mockery of sci.math, and sci.physics.
> >
> > On Monday, March 14, 2022 at 8:17:12 AM UTC-5, Timothy Golden wrote:
> > > On Sunday, March 13, 2022 at 7:54:25 PM UTC-4, The Starmaker wrote:
> > > > On Thu, 10 Mar 2022 11:57:35 -0800, The Starmaker
> > > > <star...@ix.netcom.com> wrote:
> > > >
> > > > >They keep asking the question..."What is Putin's end game?"
> > > > >
> > > > >The answer is simple...To Rule The World!
> > > > Now, To Rule The World, one needs to acquire as many nations as
> > > > possible.
> > > >
> > > > That means Putin needs to invade Paris, France and all the other
> > > > states around it...
> > > No. When Europe distances itself from the U.S. all will be well.
> > > Do you think Syrian refugees; Libyan refugees; Iraqi refugees are helping the situation? Ukranian refugees?
> > >
> > > When Europe stands up for itself the situation will be different.
> > > We will know the truth of the situation now in the future.
> > > The information served hot is corrupt.
> > > I guarantee it.
> > > How?
> > > We are saturated in U.$. lies.
> > > Frog, pot, low heat...
> > > As to who ultimately is driving this machine: I have no idea; maybe nobody.
> > > That is the scariest thought. Given Russiagate and the necessity of Biden writing the history of this era... how strange that it all would pivot around an obscure country like Ukraine.
> > >

Get a hold of this shithead-- Timothy Golden -- saying any country is obscure. Let alone a big magnificent country like Ukraine. Tim should be kicked out of sci. newsgroups as a Russian propaganda nutjob.




> > > In time I think we will see the truth here so long as they can prevent infiltration:
> >
> > > >
> > > > in other words, Putin needs to invade and acquire all the states...
> > > >
> > > > The United States of Europe.
> > > > --
> > > > The Starmaker -- To question the unquestionable, ask the unaskable,
> > > > to think the unthinkable, mention the unmentionable, and challenge
> > > > the unchallengeable.
> >
> >
> > On Wednesday, March 19, 2014 at 6:36:27 PM UTC-5, The Starmaker wrote:
> > > TThe only people I know who can tell you where the missing plane is are movie stars, tv celebrities..
> > >
> >
> > >
> > > The Starmaker
> > >
> > >
> > > Stars know everything.
> > >
> > >
> > >
> > > But what do scientist know?
> > >
> > >
> > > How many scientists does it take to change a light bulb?
> > > None. They use them as controls in double blind trials.
> > >
> > >
> > > How many physicists does it take to change a light bulb?
> > > Only one, but 600 applied for the job.
> > >
> > >
> > > How many nuclear engineers does it take to change a light bulb?
> > > Seven. One to install the new bulb and six to figure out what to do with the old one for the next 10,000 years.
> > >
> > > How many NASA technicians does it take to change a light bulb?
> > > Seventy, and they plan it for two weeks and when they finally get around to it the weather's bad so
> > > they postpone it till next week. Then Congress cuts the funding.
> >
> >
> > No wonder sci.physics and sci.math were destroyed by 1996, when all of Usenet was "run through by police drag net spam, mocking science, mocking posters" Kibo Parry Moron, king of mockery and anti-science, and paid for by CIA, FBI.
> >
> > Why, at CIA and FBI, they still believe 938 is 12% short of 945 and they still teach b.s. that slant cut in cone is a ellipse when in truth it is a Oval. So dumb in reasoning is the CIA, FBI, that none there can do a geometry proof of Fundamental Theorem of Calculus. And when you ask anyone at CIA or FBI, like Kibo Parry Moron which is the atom's true electron, muon or 0.5MeV particle, they are so much a moron, that they cannot understand the question.
> >
> > But some progress has been made on the moron Kibo Parry, for his attacks have been limited to 1 attack per day-- still- too much. William Burns, and Chris Wray, you have to pull your barking fuckdog Kibo Parry to 0 attack posts per day.
> >
> > Kibo Parry Moron blowing his cover with the CIA in 1997
> > Re: Archimedes Vanadium, America's most beloved poster
> > On Sunday, June 8, 1997 at 2:00:00 AM UTC-5, Scott Dorsey wrote:
> > > In article <5nefan$i06$9...@news.thecia.net> kibo greps <ki...@shell.thecia.net> writes:
> > > >
> > > >http://www.netscum.net/fieldsm0.html
> > > What the hell is this? As if it's not bad enough that we have a fake
> > > Mao Zhedong here, now we have a fake kibo too?
> > > Is there a fake xibo and a ~ibo to round out the trinity?
> > > --scott
> > > --
> > > "C'est un Nagra. C'est suisse, et tres, tres precis."
> >
> >
> >
> > On Wednesday, December 6, 2017 at 12:30:22 AM UTC-6, Michael Moroney wrote:
> > > Silly boy, that's off by more than 12.6 MeV, or 12% of the mass of a muon.
> > > Hardly "exactly" 9 muons.
> > Wednesday, December 6, 2017 at 9:52:21 AM UTC-6, Michael Moroney wrote:
> > > Or, 938.2720813/105.6583745 = 8.88024338572. A proton is about the mass
> > > of 8.88 muons, not 9. About 12% short.

[Timothy Golden]

Incredible how lame your response was AP.
You seem to have no regard for the rhetorical as theater.
Rather you lack the integrity to use it as such.
It is to be served on the side, like wasabi with salmon.
It should be sharp and hot to boot.
You've simply fallen for my wasabi straight into the ditch I'd say.
It's like a cop maced you in the face.
Or a girl in the park you looked the wrong way at.

So much poor grade communication takes place here by some of the most prolific posters.
I like your 'Decimal Grid Numbers' title, but they've always been that way.
As to where you put unity on your staircase: that is the job of the decimal point.
In these infinite forms we are stepping at unity on the naturals and only inductive logic gets us through.
Tripping up on double induction so early is like tying your shoes at the same time singlehanded but you wound up tying them to each other.
It's really not good, sir.
Too much wasabi, perhaps?

On Saturday, August 6, 2022 at 10:33:09 PM UTC-4, Archimedes Plutonium wrote:
> Still, the Timothy Golden nutjob steals the math work of AP, and tries to cover it up in b.s.

[Timothy Golden]

On Monday, June 6, 2022 at 5:11:17 PM UTC-4, Timothy Golden wrote:
> On Monday, June 6, 2022 at 11:53:38 AM UTC-4, Ross A. Finlayson wrote:
> > On Monday, June 6, 2022 at 6:55:21 AM UTC-7, timba...@gmail.com wrote:
> > > On Saturday, June 4, 2022 at 11:15:32 AM UTC-4, Timothy Golden wrote:
> > > > On Friday, June 3, 2022 at 11:35:51 AM UTC-4, Ross A. Finlayson wrote:
> > > > > On Friday, June 3, 2022 at 7:28:19 AM UTC-7, timba...@gmail.com wrote:
> > > > > > On Friday, June 3, 2022 at 2:15:12 AM UTC-4, Chris M. Thomasson wrote:

> > > > > > > On 6/1/2022 7:47 AM, Timothy Golden wrote:
> > > > > > > > Is 0.333... a valid number?

> > > > > > > [...]
> > > > > > >
> > > > > > > Is this a valid number?
> > > > > > >
> > > > > > > [0] = rand_range(0, 9)
> > > > > > > [1] = rand_range(0, 9)
> > > > > > > ...
> > > > > > >
> > > > > > > We can get:
> > > > > > >
> > > > > > > .218575540978324672654
> > > > > > >
> > > > > > > or anything else...
> > > > > > >
> > > > > > > ;^)
> > > > > > >
> > > > > > > Each digit is a random number for the arity of the system. So base 10
> > > > > > > (10-ary), 0-9 random numbers for each digit...
> > > > > > >
> > > > > > > We can go for infinity... Is there a limit? Humm... No? ;^)
> > > > > > It is worth pondering the random digit value as you are trying to do. As well there are nonrandoms such as the irrational solution for sqrt(2.0) which arguably do have specific digits. The ones though which are already in use are the repeating decimals, and the usage of ellipses there works out consistently. To claim that every digit is well defined seems quite readily understood:
> > > > > > 333...3546
> > > > > > as a valid constant infinite value shows we can easily work the tail of the value. Can it be said that:
> > > > > > 333...3546 = 333...3545 + 1 ?
> > > > > > I think so. This appears to be valid. To state that
> > > > > > 333...3546 = 333...3546
> > > > > > as well seems valid. If this were not so then there could be serious trouble. Somewhere along the way though as we push this interpretation something will break. Still, because the natural numbers are so primitively defined through the successor these values don't necessarily have to go through this much:
> > > > > > 111...11134 + 222...21 = 333...355
> > > > > > though even this seems uncontroversial. Multiplication even somewhat can take on its full meaning, but this will not be so easy will it?
> > > > > > ( 222...22)( 3) = 666...66
> > > > > > well, that wasn't painful, was it? With the help of sage, and the ever strange system of repeating digits which we generally gloss over I see that:
> > > > > > ( 222...22)(11) = 2444...442
> > > > > > and no doubt that could be readily proven. Induction will probably serve us nicely here in the long run. Now for the jaw breaker:
> > > > > > (222...22)(333...33) = 740740740...740259259259...259
> > > > > > and so the first double ellipsis is born and as well a discussion of the number of digits exposes that with the multiplication we are duly representing the increase of the digits with the second ellipsis. If we are going to play in aleph land as A digits then we have 2A digits for this product.
> > > > > > So there is plenty to work on here.
> > > > > >
> > > > > > It's not really my cup of tea, but I do drink tea from time to time. I even like to pick my own tea when I am doing well. Springtime is a fine time for raspberry and blackberry. You go home with your hands stained green and oily from the fresh shoots. Dry them on a screen in the attic and you've got a year or two's supply in a couple hours of work when the right patch is found.
> > > > > >
> > > > > > To be convincing here we have to cover the ground, and Chris ,you are doing that. Possibly the correct random value is well defined at both ends so that a proper instance might be more like:
> > > > > > d1 d2 d3 ... d3 d2 d1
> > > > > > where d(n) is random. Is redundancy necessary? Redundancy in nature is well supported so at least there is physical correspondence. As to whether they are computable I can't really say. Here is a neat square:
> > > > > > (222...22)(222..22) = 493827160...493827160 49382 61728 395061728...395061728 4
> > > > > > Hmmm... There's a bit of confusion on my part as to how to write this. Multiple representations of the same value are not necessarily desirable.
> > > > > > Above I've compressed the usual tripling of the repeating sequence and inserted spaces for consistency.
> > > > > > Still, by sage induction I'm pretty sure this value will hold up. I checked it at three different levels this being the longest:
> > > > > > sage: 22222222222222222222222222222222222222222222222222222222222222222222222222
> > > > > > ....: 22222222222222222222222222222222222222222222222222222222222222222222222222
> > > > > > ....: 22222222222222222222222222222222222222222222222222222222222222222222222222
> > > > > > ....: *2222222222222222222222222222222222222222222222222222222222222222222222222
> > > > > > ....: 22222222222222222222222222222222222222222222222222222222222222222222222222
> > > > > > ....: 22222222222222222222222222222222222222222222222222222222222222222222222222
> > > > > > ....: 2
> > > > > > 49382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617284
> > > > > >
> > > > > > So for all that blathering about infinities and infinities of infinities it seems there could be quite a lot to do there.
> > > > > > I'd rather not actually, but since nobody else will I'll go ahead and demo it. I think possibly I am getting to the point of the grammatical meaning of 'of' within mathematics as a term of generalization. That's more to the point.
> > > > > >
> > > > > > On the other side of the infinite instances lays the finite instances and they are plenty good. This long one up above is fine. Epsilon/delta functions long before we get this far. The rational value fails out of the gate. It is the decimal value and its unity interpretation which gets us the continuum. Pushing farther on unity interpretations we can have a bit more, but the dirty reradixer is trouble. As we agree by convention to work in one radix then to push another without explicitly stating it to be so is problematic. This is built into the nature of the rational value.
> > > > > These numbers of course with "many or slowly repeated a terminus, then a
> > > > > different one for example zero", ..., "rational", is for roots it seems, powers
> > > > > under roots or for primary functions, result measures, boxes, frames, ....
> > > > >
> > > > > You then have them related this way, in terms of values, and either what
> > > > > they parameterize or how they are parameterized, "numbers".
> > > > >
> > > > > Here when you say radix, it's the representation also the fixed-point,
> > > > > whether .111... is the radix or 1 is the radix, just to point out that the
> > > > > term "radix" is overloaded, in terms of elements of the field or fractions,
> > > > > and elements of the iota-values or increments.
> > > > >
> > > > > ... For example when the field is large, but finite.
> > > > There is something wrong with the square of 222...22. I put one extra 2 on each product from the long instance I gave and the middle nonrepeating digits turned from 61728 to 7061728. So it's not quite right there in the middle. It's been consistent other than that though.
> > > >
> > > > Putting on one additional 2 I now have 715061728 for the center digits. Plodding along finally at
> > > > a=2222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222
> > > >
> > > > we get clean and there is no middle digit conundrum. That's 226 twos. On intervals of nine twos. Perfect again at 217 twos.
> > > > Given the digital redundancies I think it is fair to claim that the square of 222...2 is:
> > > > 493827160...395061728...4
> > > > where again I've compressed the notation down to something that is not so redundant but can be decoded given the earlier work. Given the extensive use of repeating digits this format is better. It happens not to need any spacing but space would allow say for a unique head in any position.
> > > >
> > > A less controversial solution exists on 333...3 whose square is:
> > > 111...10888...89
> > > or in short spaced form:
> > > 1... 0 8... 9
> > > and no controversy seems to ensue starting at a=33 where aa = 1089.
> > >
> > > The effect of the product in raising the quantity of digits is something ignored in abstract algebra. They insist upon an infinite length polynomial to hide this, yet it is clearly a fake formality. To correctly account for their infinity of zeros after a product is taken there should be two sets of ellipses. Otherwise they've screwed aleph. So this numerical analysis does expose something beyond its own construction. If we bridge number theory at this primitive level with the polynomial and even into its abstract form the glue that binds these things exposes that infinite length strings are not only in use in higher mathematics, but they are insisted upon, particularly in abstract algebra.
> > >
> > > Again a choice can be made to reject this usage or to go ahead with it. Each choice has consequences. Either way abstract algebra is broken.
> > > > It seems like these infinite forms are getting more informational. There has been a process of reduction here that is not uncommon in other mathematics. We like to work with the simplest form and I believe I did prove it. possibly a formal proof would look a bit different, but the mechanics as stable here allow for induction to take place. There are eight other forms of this value and since we are in a weird new form could it be that there are nine squares of 222...2? Surely this is a side-effect of the radix that we work in. When we blame the value rather than the radix... well possibly that is when the dirty reradixer finds his way.
> > > >
> > > > With ten twos (a = 2222222222) we see
> > > > a*a = 4938271603950617284
> > > > which is the first clean instance though no repetition occurs. Somehow this is a reduction of an infinite system worked in base ten.
> > > > Insert some ellipses in the correct locations and the infinite form is available; not unlike the insertion of a decimal point to beget the continuous value. I think as one starts into this infinite form we see that a new sort of grammar emerges. I don't think it is general yet, but it is emerging simply through usage. To state that these infinite forms are highly redundant is a necessary predicament, yet to which physical correspondence does hold.
> > > >
> > > > It might merely be a place to get lost in. It might not be wise to entertain these things seriously, yet in the quantity of ground that could be covered these are possibilities. We have demonstrated an ability to square an infinite value here. The computation is digital in nature.
> > It's interesting what is "effective infinity" or the limits of precision, where any
> > point is both at the center of an oriented lattice, and of a sphere.
> >
> > When you mention digital then there's Wolfram's massive "A New Kind of Science",
> > it's very much about the development of cellular automata, which in a sense describe
> > the same evolution in series but "always granular" instead of "ever fine".
> a = 111...1
> is pretty tricky squared:
> 123456790... 098765432... 1
> and there are ambiguities in the middle along the way, but this is the clean solution.
> The cube suddenly turns horrendously long:
> 137174211248285322359396433470507544581618655692729766803840877914951989026063100...
> 392318244170096021947873799725651577503429355281207133058984910836762688614540466...
> 470507544581618655692729766803840877914951989026063100137174211248285322359396433... 1

It may be an important detail that while the quantity of digits appears larger here it is not any larger than the simpler instances. The ellipses belie the aleph quality of each of these 'segments' of this infinite value. It is true that their complexity is greater, but their quantity is not.
The number of (potential) digits of the resultant of a product is the number of digits of the arguments of that product.

>
> Troubling especially since embedded in the last repetition is the first repetition.
>
> The NKS algorithm is awfully primitive. That does bring time into the discussion I think.
> It seems like the mathematicians avoid time. So do the cosmologists. Their first principle is that space is isotropic; not that spacetime is isotropic. So does this mean that spacetime is structured? Nice discussion they are not having on this.
>
> What is good about NKS is emergence. At the early stages we should accept any emergence as progress so it deserves credit. At some point we want to demand emergent atoms with the exact spectroscopic properties, exact isotopes, and so on as we witness in nature. As to how much of physics is sitting upon empirical data: this limits how far theory can get. Theory is lagging way behind experimental physics. This position rejects curve-fitting as theoretical.
>
> If we establish an emergent form of spacetime then isn't there cause for hope?

[Ross A. Finlayson]

It makes sense "while keeping my scientific numbers and
correctly zero-ing out what cannot be kept by rounding,
the science of rounding describes for the error term in
rounding, why to keep around the products of the most
significant products in terms their log, keeping track
of rounding in bounds".

Then for resulting "well though it's not interval arithmetic
itself there's attached these bounds in rounding", then for
example, gets to where "according to these roundings in
bounds, I _might_ have reached a perfect number, while
the rounding is still less than it". I.e., "at the same time I
add up for what divides down from it pi or e, arriving at
bounds for a perfect number, it finds the middle of the
rounding bounds, as an estimate for the rational input".

Or 1.0 for example, "1.000..." here, "effectively unbounded-
precision numbers".

Then for example for running that through and seeing
that it adds up: log-bound products in terms, for example
constant access after linear time, and that continuing in
linear time builds a bigger number (or product of diminishing
terms, diminishing by their bounds), is an exercise in an:
arithmetic coding.

[Jame Cuocco]

Ross A. Finlayson wrote:

> It makes sense "while keeping my scientific numbers and correctly
> zero-ing out what cannot be kept by rounding,
> the science of rounding describes for the error term in rounding, why to
> keep around the products of the most significant products in terms their
> log, keeping track of rounding in bounds".

nonsense. This is incorrect. What they want is not 95% depopulation, but a
reduction to about 500,000, whereof 250k would be the workers, they need
workers, then the rest 250k are the capitalist oligarchs.

so a 500k out of 8 bil, in percents 5/800 which gives 0.0006%. So the
oligarchs of america want to kill 99.9994% of the world population. For
the climate concerns. If you think you are lucky, you are a fool.

[Ross A. Finlayson]

This is for log and lossage and e and gain,
ln and e, that ln e = 1.

[Timothy Golden]

I think the physicists arrive at notation like 1.234(56)
which leaves the six as meaningless other than for further computations.
In engineering classes we simply treated the last digit as I believe the 4 in the above example. It would become a 5 by the rules of rounding.
I did just go to verify this claim, and it might be wrong, but to admit that the perfection of numbers is not necessary is clear. That the numbers go gray and unknown; even spinning like little wheels grayer and grayer down the line; this at least gives these imperfect forms some life and quality.

Now for the side track: https://en.wikipedia.org/wiki/Strong_CP_problem

[Mostowski Collapse]

Frank was always great at math. I didn’t take any math
past high school, myself, and only then just took the bare
minimum. But hey, I’m a writer, what do I need math for?
Don’t get me wrong, I use algebra and some very basic
geometry. But a tangent? That’s like, what, one of those
functions like sine and cosine? I can’t even remember
what those are. I’ve never needed them. Ever. Why do
they make kids take that stuff? It shouldn’t be required.

timba...@gmail.com schrieb am Mittwoch, 1. Juni 2022 um 16:47:12 UTC+2:
> Is 0.333... a valid number?

> If so then by the structural argument the title's answer is yes.
> The decimal place is obviously a structural augmentation to the natural value.
> A long string of digits is all that is left to digest.
> Well there is slightly more. Are numbers two-sided?
> Isn't this cause to reject the usual decimal representation of 1/3 and insist instead upon:
> 1/3 = 0.333...3
> to secure the rhs? Now we have the initially built natural value though it is in an infinite form.
>

[Mostowski Collapse]

That’s the thing with Frank. He’s only into what he’s into.
Doesn’t really care about other people. Maybe that’s why
he’s been divorced four times. Yeah, that’s right, FOUR TIMES!
You’d think by now he would have learned his lesson, but nooooo…
he’s engaged right now. And let me tell you, everybody but them
can see it’s never going to work. They fight all the time, and I mean
constantly. It’s getting to where nobody wants to invite them.

[michael Rodriguez]

> ...and without commas- :))
https://groups.google.com/g/sci.math/c/XddodYR-h08

;)

[zelos...@gmail.com]

Prove it

[Timothy Golden]

On Wednesday, August 24, 2022 at 6:13:08 PM UTC-4, Mostowski Collapse wrote:
> Frank was always great at math. I didn’t take any math
> past high school, myself, and only then just took the bare
> minimum. But hey, I’m a writer, what do I need math for?
> Don’t get me wrong, I use algebra and some very basic
> geometry. But a tangent? That’s like, what, one of those
> functions like sine and cosine? I can’t even remember
> what those are. I’ve never needed them. Ever. Why do
> they make kids take that stuff? It shouldn’t be required.

There is plenty to discuss. Plenty of content here.
You've decided to pipe up with nothing.
If you are feeling vacuous maybe it is time to review some basics.
The details discussed here are of fundamental nature.
The natural value as secure beneath all decimal representations is well founded, though the realization seems new.
That we need but one natural value, and a placeholder for unity: this is a structural argument.
It bypasses the rational value completely, which deserves exactly this treatment.
If the continuum is some magical pairing of two natural values then Mostowski Collapse is not as brilliant as he thinks he is.

[Eram semper recta]

On Friday, 3 June 2022 at 01:29:55 UTC-4, zelos malum driveled:

> onsdag 1 juni 2022 kl. 16:47:12 UTC+2 skrev timba...@gmail.com:
> > Is 0.333... a valid number?

> {s}yes{/s}

NO.

A number is the measure of a ratio, in particular, the antecedent part of a ratio that is measured by its consequent.

https://www.academia.edu/69488136/Theory_of_fractions_from_Book_5_of_Elements_for_Dummies

0.333... is just a string of 4 digits followed by an ellipsis and it is shorthand for the *FINITE* series 0.3+0.03+0.003+...

> > If so then by the structural argument the title's answer is yes.

> Given it has finite number of 3s then yes, it is also valid.
>
> If you meant ...33334 on the other hand with infinite 3's, then you are wrong and the two are not equivalent.

> > The decimal place is obviously a structural augmentation to the natural value.

> {s} No, it is just notatoin. {/s}

The decimal notation is a failed attempt at measuring 1/3 in base 10. Learn more:

https://www.academia.edu/39981684/Proof_of_the_most_important_Number_theorem_that_mainstream_mathematics_academics_never_learned

1/3 has no representation in base 10. It's much like pi or square root 2 in decimal - all have no measure.

> > A long string of digits is all that is left to digest.

> {s} any finite number of digits is valid.{/s}

No! 0.333 to as many places as you like NEVER represents 1/3 in base 10 just as 3.14159 taken to as many places as you like NEVER represents the *CONSTAN* pi in base 10. In the case of pi, it cannot be represented (measured) in any radix system which is generally true for any ratio that has no measure. Pi is realised from the ratio circumference : diameter.

> > Well there is slightly more. Are numbers two-sided?
> > Isn't this cause to reject the usual decimal representation of 1/3 and insist instead upon:
> > 1/3 = 0.333...3

{s}Nope, stop being a crank.{/s}

No, because as I explained to you, radix representation is not possible for all numbers, that is, for any number p/q to be representable (measurable) in base b, you need that 2 and 5 are factors of b. THIS AND NOTHING ELSE.

> > to secure the rhs? Now we have the initially built natural value though it is in an infinite form.
> >
> > To argue that the value of the digits are infinitessimal in the 1/3 instance does nothing to the informational representation. Likewise epsilon/delta will suffice just as it does for the irrational values as Dedekind presented it. The fact that the digits are redundant is handy. Still better if we went to modulo three representation one third would simply be 0.1 and so no puzzle even ensues.
> >
> > For those who like infinity I would think they'd like to let in this infinite value representation of a natural value.

>{s} They work in other number systems, just not reals. Educate yourself. look up p-adic numbers.{/s}

Sonny, in the Church of Academia they have strict decrees. Your flavour of bullshit doesn't smell as good as theirs. Chuckle.

[Eram semper recta]

Sorry: 2 and 5 are factors of q and b.

[Mostowski Collapse]

Isolated on his fish mission, Frank finds himself stuck
behind police tape, happily munching from his grease-
slicked paper bag of the Gang’s food. Frank is often odd
Gang member out, his age and own particularly atavistic
brand of awfulness sending him scurrying on a parallel, if
somehow more ridiculously grubby journey to the rest.

Frank never means to suggest to the obliging officer
that he’s the father of the poor sap on the roof, but is,
instead, just babbling about his actual (sort-of) son
Dennis “doing something stupid” like, for example,
dropping his prized sex-melon on the floor.

Meanwhile, Frank, digging his fingers grotesquely into
that melon-hole, reveals that that’s where he hides his
weed. (“Pot’s pretty much legal now, man,” observes Mac.)
Oh, and he totally does have sex with it, as he, taking a
bong hit, helpfully advises the hungry Cricket, “I wouldn’t
eat it, Cricks. It’s full o’ loads.”

[Mostowski Collapse]

That’s something Frank came to understand only
later on, when he returned to Prague during the Spring and
Asylum was still going strong. Once he realized that, I don’t
know if he was more nonplussed coming to terms with the
circumstances of his departure or the fact that Asylum could
function without him. Either way I think he was justifiably proud
of the fact that he had been the driving force behind the creation
of something truly beautiful and communal.

As an added dividend of this approach he did also obtain the
existence of canonical isomorphisms of the de Rham and differentiable
singular cohomology theories with the continuous singular theory,
the Alexander-Spanier theory, and the Cech cohomology theory for
differentiable manifolds. From these isomorphisms he concluded
that the de Rham cohomology theory is a topological invariant of
a differentiable manifold.

[michael Rodriguez]

> That’s the thing with Frank. He’s only into what he’s into.
> Doesn’t really care about other people. Maybe that’s why
> he’s been divorced four times. Yeah, that’s right, FOUR TIMES!
> You’d think by now he would have learned his lesson, but nooooo…
> he’s engaged right now. And let me tell you, everybody but them
> can see it’s never going to work. They fight all the time, and I mean
> constantly. It’s getting to where nobody wants to invite them.

It needs the other frank
Frank Kermit - Emotional Needs Of Women https://www.youtube.com/watch?v=kGY-jKjTN84
https://www.youtube.com/watch?v=iB67fx6RMb8

;0

[Mostowski Collapse]

The executive summary of Fanks Pizza gives a vivid of
a system that will be linked to the current point-of-sale
system. I think the author of the plan intended to explain
that the primary role of the new system is to help identify
potential markets and separate them from markets that the
management need to do extra promotions.

The hyperspectral IMS data is typically generated by a mass
spectrometer analyzing the surface of the sample. In this
paper, we propose a compressed sensing approach to IMS
which potentially allows for faster data acquisition by collecting
only a part of the pixels in the hyperspectral image and reconstructing
the full image from this data.

[Russ Messana]

Mostowski Collapse wrote:

> The hyperspectral IMS data is typically generated by a mass spectrometer
> analyzing the surface of the sample. In this paper, we propose a

gearmon nazis saying the Russians using *selling_natural_gas* as weapon of
war, meanwhile the gearmon nazis are using tanks as weapons to kill
Russians.

Scary： ZSU Gepard 1A From Germany Now In AFU's Hands In Donetsk
https://www.bitchute.com/video/xBCAKKpsxl4P/

how the fuck are the Russian going to forget this shit, I have no idea.

[Mostowski Collapse]

Congratulations ruZZbot! The honey pot worked.
https://en.wikipedia.org/wiki/Honeypot_(computing)

LoL

You are quite a stalker! BTW: I could go on and on:

Finally heading to Vernazza Frank meets heroic wine producers
Bartolo and Lisse who scale 1000 meters above sea level to tend
to their vines! Frank prepares a tiramisu with a twist - using lemons
and limoncello. Perfect with a glass of local dessert wine, and
for steadying the nerves!

At ESA's ESTEC centre near Amsterdam and at CERN in Geneva
Frank is trying to explore 'The Dark Side', the mysterious forces
of dark matter and dark energy which are thought to rule the cosmos.
The Euclid space telescope will soon offer him a unique point of
view while on the ground, looking at the atom level, the particles
accelerator can offer new observations.

[Bowen Rapallino]

Mostowski Collapse wrote:

> Congratulations ruZZbot! The honey pot worked.

in *fake_money* capitalism you are going to use *washcloths*, you stupid
irrelevant nazi shit.

the fake capitalist doctor, distributing the money of state in *billions*,
the khazar fauci, is ready to depopulate your ass from different
direction.

GLOBALISTS Culling The Human Herd
https://www.bitchute.com/video/rkdQYnawbJ7v/

stay cool.

[Mostowski Collapse]

Woa! ruZZbot, you are kind of repeating yourself.
Looks like you are muito louco mesmo?

LMAO!

[Mostowski Collapse]

Why are Russians so weird?
https://www.rbth.com/lifestyle/328910-why-russians-are-so-weird

“Russians are weird because while you complain
about a 3 hour flight that didn’t have a vegan meal
option, they were traveling to and from Siberia in a
train for a week one way with nothing but a t-shirt, a
change of underwear, a pack of cigarettes and a few
boxes of instant ramen,” Thomas Hulber, who lives
in Russia, and claims that he has “seen some stuff”,
wrote on Quora.

They also can do this “weird” thing with “mat”, where
they can, through joining roots, turn almost every word
of a sentence into a swear. Like “Abso-freaking-lutely”,
but for every word! Weird, sure, but also neat if crude,”
Murphy Barrett writes. Among Russian, that latte
thing is called “the three-storeyed swearing”, when
you not only use the most rude words, also you invent
new rude words from usual.

Some superstitions, however, come from very rational
reasons. It is believed that spilling salt would cause
an argument – naturally so, because up until 19th
century, prices for salt were very high – it’s a natural
conservant that helped preserve foods for long winters.
And this habit of putting empty bottles under the table
came from times when bills in inns and bars depended
on the amount of empty bottles on the table.

[Lettucio Van Picklish]

> That’s the thing with Frank. He’s only into what he’s into.
> Doesn’t really care about other people. Maybe that’s why
> he’s been divorced four times. Yeah, that’s right, FOUR TIMES!
> You’d think by now he would have learned his lesson, but nooooo…
> he’s engaged right now. And let me tell you, everybody but them
> can see it’s never going to work. They fight all the time, and I mean
> constantly. It’s getting to where nobody wants to invite them.

if muhammad does not go to the mountain the mountain goes to muhammad. The frank guy will make it.
Instead ofgo into an arbitrary use of https://en.wikipedia.org/wiki/Hyperspectral_imaging#Applications
he may manage to biuld a machine that detect the hormonal states of his partner in order
to be able to "read the signs" of her sweetie. A sort of Venusian translator.

;0

[Mostowski Collapse]

In his early 20s, Frank seemed to have everything
one could wish for: a funded degree in industrial
engineering with excellent achievements and
international career prospects at one of the most
respected transport companies in the world.

Viewed from the outside, life is in the fast lane towards
the social ideal. Inwardly a fast track to the dead end.
Severe depression, attempted suicide, closed psychiatric
ward and all that in the prime of life at the age of 23.

[Mostowski Collapse]

Frank thought why Pi ? Pi is the ratio of the circumference of a
circle to its diameter. Pi is a transcendental and irrational number.
Pi has been calculated beyond one trillion digits past its decimal
point without repetition or pattern. It is the epitome
of randomness.

What comes before has no influence on what comes next,
there is no evident structure or pattern. It appears to be
infinite and random yet it embodies order inherent in a
perfect circle. The beauty of pi, is that it puts
infinity within reach.