0 = 1

[conway]

0 and 1 share identical spaces. ( 1 + (-1) ) proves this....if 0 did not have a space on the number line the equation would equal -1. 0 and 1 do NOT share a value in common. 0 is NOT equal to 1. according to value. But according to space they ARE equivalent.

0(as a number) Is NOT = 1(as a number)
0(as value) Is NOT = 1 (as value)


0(as spaces) = 1 (as space)

an empty space is still a thing, it is NOT nothing...it can be measured and interacted with......so should zero.

[konyberg]

Hi.
Aren't you confusing a number line with a time line?
KON

[Jens Stuckelberger]

I hope that the relevant committee will award this ground-
breaking development, that fills a very much needed gap, with this year's
Fields Medal.

[conway]

Karl

Hi...I don't believe so. Firstly...I've never seen a time line of any kind involving integers(negatives). Secondly...the expression (1 + (-1)) can be graphed. Graphs are number lines.....sometimes used to represent "time" lines. In any case when I graph the given equation I for a FACT land on the SPACE of 0. Therefore 0 has SPACE, and its space is equivalent to 1.

[Bill]

By "gap" do you mean a "space"?

[zelos...@outlook.com]

Define what you mean with space here as otherwise it is non-sense.

[dylan.y...@gmail.com]

0 is not "nothing" it's 0.

[Dan Christensen]

Looks like you have found a bug in your system, Conway. You had better fix that.


Dan

[conway]

zelos


Excellent question....


space is a given quantity of dimension

value is a given quantity of existence other than dimension


here it is visually

space of 2 = (_,_) = z1
value of 2 = (1,1) = z2
the number 2 = (z1 + z2)


Dylan

It is obviously 0 is 0. What is it's constituents? What is it made up of? You agreed it is not nothings.....so then 0 is space.


Dan


Care to explain?

[Dan Christensen]

On Thursday, September 7, 2017 at 10:40:13 AM UTC-4, conway wrote:

> Dan
>
>
> Care to explain?

If you can obtain 0=1 in your system, there is clearly something wrong with it and you must fix it.

Example from my own experience: In an early test version of my DC Proof program, I was able to "prove" that every set was an empty set. Now, I didn't pretend that I had discovered some great truth about set theory and go on some crazy crusade to bring down the mathematical establishment. I fixed the problem -- a subtle error in my Subset Axiom.


Dan

Download my DC Proof 2.0 software at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com

[conway]

Dan


If you had read....if you had understood....you would have known that I made the point that only a "piece" of zero is equal to one. As a number they are NOT equal. The title is "truthful". And there is NOT a contradiction.....again...


0(as a number) is NOT = 1 (as a number)
0(as space) = 1 (as space)

You need to at least be fair here. You constantly spout off retorts without actually grasping what it is that I have said. I apologize for being controversial. It is my right....further I do so in an appropriate manner (unlike JG)... and the right place. Stick to bullying JG...you do it so well.....

[Dan Christensen]

On Thursday, September 7, 2017 at 1:50:13 PM UTC-4, conway wrote:
> Dan
>
>
> If you had read....if you had understood....you would have known that I made the point that only a "piece" of zero is equal to one.

That's were really seem to lose it, Conway.

> As a number they are NOT equal. The title is "truthful". And there is NOT a contradiction.....again...
>
>
> 0(as a number) is NOT = 1 (as a number)
> 0(as space) = 1 (as space)
>

No amount of hand waving will convince knowledgeable people that 0=1. And none are particularly troubled by the fact that there is no solution to 0x=1. They understand that 1/x increases without limit as x tends to 0 from the right, and that it is undefined when x=0. They also understand that 1/x decreases without limit as x tends to 0 from the left. And it has nothing to do with your supposed solutions to 0x=1.

> You need to at least be fair here. You constantly spout off retorts without actually grasping what it is that I have said.

Seeing your end results, I am not particularly motivated to untangle your twisted logic -- an informal garble of symbols that looks only vaguely mathematical. You have also ignored requests to formalize your system. I'm not sure that you even understand what that means.

[Peter Percival]

conway wrote:

> 0(as a number) is NOT = 1 (as a number)
> 0(as space) = 1 (as space)
>

What is space in this sense?


--
Do, as a concession to my poor wits, Lord Darlington, just explain
to me what you really mean.
I think I had better not, Duchess. Nowadays to be intelligible is
to be found out. -- Oscar Wilde, Lady Windermere's Fan

[conway]

Dan

For a FACT....I formalized the system. I wrote an axiom (can't get more formal than that). My hands are waving, but my logic is not garbled. It is your sense of wonder and imagination that is garbled. I will continue to post, and I will begin to ignore you. You have zero academic honesty. Anyone can see this reflected in your post.


Peter

Same as it was in my other posts. Space is a quantity of dimension. I know your thoughts on this....no need to respond to me anymore

[Dan Christensen]

On Thursday, September 7, 2017 at 5:10:13 PM UTC-4, conway wrote:
> Dan
>
> For a FACT....I formalized the system. I wrote an axiom (can't get more formal than that).

I think you may have informally stated some axiom(s), but that won't do in this context.

Perhaps you need an example. Here is the most commonly used formal axioms for the set of natural numbers:

1. 0 in N
2. For all x in N: S(x) in N
3. For all x, y in N: [S(x)=S(y) => x=y]
4. For all x in N: S(x)=/=0
5. For subsets P of N: [0 in N & For x in N: S(x) in N => P=N]

Do you think you can write your axioms in this form?

> My hands are waving, but my logic is not garbled. It is your sense of wonder and imagination that is garbled. I will continue to post, and I will begin to ignore you.

That's fine with me.

> You have zero academic honesty.

You have zero mental discipline. You can't just make things up willy-nilly just because they sound cool. You must do your homework.

>
>
> Peter
>
> Same as it was in my other posts. Space is a quantity of dimension.

This might suffice for a dictionary definition, but it is quite useless for doing mathematics. Really quite garbled. Your proposed theory needs a LOT of work, Conway.

[Me]

[conway]

Dan....

You are starting to play fair. I AGREE that this idea needs a LOT of work. The fact that you are still here....suggest you know at some level "something" might here. Help me! Also I agree my logic can be "garbled". I am a philosopher. Not a mathematician. Mathematics...(indeed all the sciences) were born in philosophy. This idea makes sense. I think you see that. Until now you have refused to take it serious however because you "believe" that I have not done my homework (I have, just not the kind you like). Give me a serious....honest chance to explain this idea to you.

N = set

A = ANY number in the set


z1 = quantity of value (we can work on a more "formal" definition)

z2 = quantity of space (we can work on a more "formal" definition)

A = (z1+z2)

ANY binary expression of multiplication

z1 x z2
z2 x z1

3 x 2

z1 for 3 = 3
z2 for 3 = 3
z1 for 2 = 2
z2 for 2 = 2

3(as z1) x 2(as z2)
3(as z2) x 2(as z1)...

z1 for 1 = 1
z2 for 1 = 1

z1 for 0 = 0
z2 for 0 = 1


surely you can see there is nothing further to state using the "formal system" of axiom descriptions that you gave....other than to say the following...


For any number in N, there exist a z1 and z2 constituting that number......and so on....

[Dan Christensen]

On Thursday, September 7, 2017 at 9:40:13 PM UTC-4, conway wrote:
> Dan....
>
> You are starting to play fair. I AGREE that this idea needs a LOT of work. The fact that you are still here....suggest you know at some level "something" might here. Help me! Also I agree my logic can be "garbled". I am a philosopher. Not a mathematician. Mathematics...(indeed all the sciences) were born in philosophy. This idea makes sense. I think you see that. Until now you have refused to take it serious however because you "believe" that I have not done my homework (I have, just not the kind you like). Give me a serious....honest chance to explain this idea to you.
>
> N = set
>

Do you mean N is an arbitrary set?

> A = ANY number in the set
>

So A is an element of N that is also a number? Might there be non-numbers in N?

>
> z1 = quantity of value (we can work on a more "formal" definition)
>
> z2 = quantity of space (we can work on a more "formal" definition)
>
> A = (z1+z2)
>

So z1 and z2 are simply any pair of numbers such that A = z1+z2?

If A=2 then could we have z1 = 5 and z2 = -3?

> ANY binary expression of multiplication
>
> z1 x z2
> z2 x z1
>

Meaning?

> 3 x 2
>
> z1 for 3 = 3
> z2 for 3 = 3

Doesn't z1+z2 have to be 3?

> z1 for 2 = 2
> z2 for 2 = 2
>
> 3(as z1) x 2(as z2)
> 3(as z2) x 2(as z1)...
>
> z1 for 1 = 1
> z2 for 1 = 1
>
> z1 for 0 = 0
> z2 for 0 = 1
>

Makes no sense at all. Examples will not do in this context. We need unambiguous definitions. Maybe something of the form: For all x in R, there exists (unique ?) z1 and z2 in R such that _______________ (Fill in the blank)

But even if you manage to do this, you must show how this relationship somehow determines the real value of x where 0x=1. It's just too bizarre. Every elementary school graduate knows that 0x is always 0 for ANY real number x. There can be no doubt about this. I really can't see where you are going with this. Are you deliberately trying to create confusion and frustration among students?

[zelos...@outlook.com]

So you are saying that space is just the dimension cardinality? Why waste word and make it sound woo woo? And hten you are aboslutely wrong because 0 and 1 has no fucking dimensions

[Peter Percival]

conway wrote:


> z1 = quantity of value (we can work on a more "formal" definition)
>
> z2 = quantity of space (we can work on a more "formal" definition)

We? It's you that needs to do that.

[Peter Percival]

conway wrote:

>
> Peter
>
> Same as it was in my other posts. Space is a quantity of dimension.

That is no definition.

I know your thoughts on this....no need to respond to me anymore

Can you please learn to use Usenet properly? There is no threading and
no context.

[Peter Percival]

Dan Christensen wrote:
> On Thursday, September 7, 2017 at 5:10:13 PM UTC-4, conway wrote:

>> Same as it was in my other posts. Space is a quantity of
>> dimension.
>
>
> This might suffice for a dictionary definition,

It doesn't.

> but it is quite
> useless for doing mathematics. Really quite garbled. Your proposed
> theory needs a LOT of work, Conway.

[conway]

Dan

N = Any set what-so-ever.

A = Any number what-so-ever.

z1 is not a number to be added
z2 is not a number to be added

so saying (z1 + z2 ) is inaccurate...(apologies)(no previous way to describe this)

z1(a value) is "placed" into z2(a space)

if A = 2

z1 of A = (1,1)
z2 of A = (_,_)

put z1 into z2, you then "create" a "number", then add the numbers in all the spaces.

This is EXACTLY what all ready happens in multiplication....!

2 x 3 means.......

2 in 3 spaces then add...

2 + 2 + 2

2 is a value, it is "placed" into three "spaces" creating numbers, then all numbers are added......


I mean no misdirection to students. I think you know this. Why would a student bother with this? There is no such thing as a "false" prophet of mathematics....only ideas....wrong or right.....




for all X in R there exists a unique z1, and z2, "IN X" such that any X in a binary operation of multiplication or division is only representing z1 and z2.(of the given numbers in the binary expression)

z1 and z2 for all X other than 0 equal X

[conway]

zelos


0 and 1 both have dimension I can prove this with an expression

1 + (-1)

?

What has given you the impression that they do NOT have dimension. (1) of ANY thing has dimension. The number (1) on a piece of paper has dimension. If I have nothing.....I still have and exist in dimension. There is NOTHING and NOWHERE that does NOT have dimension.

[Peter Percival]

conway wrote:
> zelos
>
>
> 0 and 1 both have dimension I can prove this with an expression
>
> 1 + (-1)
>
> ?

The answer depends on what 1 and -1 are. If they are elements of an
additive group (which may have further structure on it) then the answer
is 0. If, on the other hand they are something else invented by you,
then it is for you to answer your own question.

>
> What has given you the impression that they do NOT have dimension.
> (1) of ANY thing has dimension. The number (1) on a piece of paper
> has dimension. If I have nothing.....I still have and exist in
> dimension. There is NOTHING and NOWHERE that does NOT have
> dimension.
>

[conway]

Peter


Why do you waste your time? You prove my point.....regarding 1 + (-1).....I never claimed they were anything else other than members of a set possessing the additive identity property.......I have only claimed that the elements of this set...that is the numbers in this expression... are composed of other things.........you are defiantly an adequate troll.........further post by you will be ignored....unless you begin to play nice.

[Bill]

Peter Percival wrote:
> conway wrote:
>
>>
>> Peter
>>
>> Same as it was in my other posts. Space is a quantity of dimension.
>
> That is no definition.

He's not a mathematician or a math student. He's just another one of
those with an axe to grind.

[konyberg]

torsdag 7. september 2017 01.00.12 UTC+2 skrev conway følgende:
> Karl
>
> Hi...I don't believe so. Firstly...I've never seen a time line of any kind involving integers(negatives). Secondly...the expression (1 + (-1)) can be graphed. Graphs are number lines.....sometimes used to represent "time" lines. In any case when I graph the given equation I for a FACT land on the SPACE of 0. Therefore 0 has SPACE, and its space is equivalent to 1.

I was thinking of the difference between a number line and a time line.
On a number line, you have the numbers ... -2 -1 0 1 2 ... as points.
In a time line you have ... -2 -1 1 2 ... as spaces (line segments). The only point on a time line is "0".
Consider years BD and years AD.

KON

[Bill]

conway wrote:
> Peter

>
> .........you are defiantly an adequate troll.........further post by you will be ignored....unless you begin to play nice.

I presume it's supposed to be a joke. conway plays the con way.

[Peter Percival]

Suit yourself, but in any case may I urge you to post to the newsgroup
using a news client and a news server? Both are available for free, and
it will make posts much easier to follow. Do you see how this post
appears as a reply to yours with your text quoted? Your posts float in
mid air with no connection to anything else.

[conway]

>
>
> Suit yourself, but in any case may I urge you to post
> to the newsgroup
> using a news client and a news server? Both are
> available for free, and
> it will make posts much easier to follow. Do you see
> how this post
> appears as a reply to yours with your text quoted?
> Your posts float in
> mid air with no connection to anything else.
> >
>
>
> --
> Do, as a concession to my poor wits, Lord Darlington,
> just explain
> to me what you really mean.
> I think I had better not, Duchess. Nowadays to be
> intelligible is
> to be found out. -- Oscar Wilde, Lady Windermere's
> Fan
>

Peter

Thank you. This is the most polite post you have managed to respond with. I understand what it is like to constantly have to deal with people and their "ideas". I understand that the probability is that I am a crank...You can chose to stop replying if you feel this is the case. But to continue to reply without academic merit and ONLY insults is a waste of OUR time.


In any case I concede that you are correct in my failure to use this forum appropriately. I will try to correct this issue thank you. Perhaps you can inform me on how to reply to a reply in a thread...as opposed to just making a new reply to a reply....


Further (IF) Dan choses to help me with definitions than "we" was an appropriate chose of words. Perhaps you can help me (us) sort this out.....if not.....please move on and let me be a crank without the your insults.....

[Markus Klyver]

How is 0 space?

[conway]

>
> I was thinking of the difference between a number
> line and a time line.
> On a number line, you have the numbers ... -2 -1 0 1
> 2 ... as points.
> In a time line you have ... -2 -1 1 2 ... as spaces
> (line segments). The only point on a time line is
> "0".
> Consider years BD and years AD.
>
> KON

Karl

I appreciate the point you have raise here. Firstly bc/ad still doesn't involve integers (negatives). But I see the point you make. I think it also makes my point. We know there was not such point as "0" time in-between 1bc and 1ad. Nor did people in 1ad refer to themselves as living in the year 1. It would have been hard for the old folks lol.....but can we show a point of 0 time at all? I say no.

[conway]

> How is 0 space?

Markus


I can "see" the space of zero on ANY number line. Anyting that is "empty" can be measured. ANY time I have zero of anything, I still posses space.

[bassam king karzeddin]

> 0 and 1 share identical spaces. ( 1 + (-1) ) proves
> this....if 0 did not have a space on the number line
> the equation would equal -1. 0 and 1 do NOT share a
> value in common. 0 is NOT equal to 1. according to
> value. But according to space they ARE equivalent.
>
> 0(as a number) Is NOT = 1(as a number)
> 0(as value) Is NOT = 1 (as value)
>
>
> 0(as spaces) = 1 (as space)
>
> an empty space is still a thing, it is NOT
> nothing...it can be measured and interacted
> with......so should zero.

The alleged topmost mathematicians on earth and from their moderated or fabricated history had proven long ago that (0 = 1), with so many DOCUMENTED references that they can't hide, and much more to this they had proven rigorously that (p = q), where (p, q) are distinct integers, for sure

BKK

[Dan Christensen]

On Wednesday, September 6, 2017 at 3:01:29 PM UTC-4, conway wrote:
> 0 and 1 share identical spaces. ( 1 + (-1) ) proves this....if 0 did not have a space on the number line the equation would equal -1. 0 and 1 do NOT share a value in common. 0 is NOT equal to 1.

Thanks for confirming that, contrary your heading, we still have 0=/=1.

> according to value. But according to space they ARE equivalent.
>

Huh??? Not sure what kind of wonky equivalence relation you have in mind, but it sure isn't equality. 0 and 1 are NOT generally interchangeable.

So, we still have 0x=0 and 0x=/=1 for all x in R. And 0=/=1. Whew!

[Markus Klyver]

This means nothing. How exactly is 0 space? Answer the question.

[conway]

Markus

Zero is a dimension that is empty. Zero is a space that is empty. Zero "on" the number has a space, and it is empty of value. Zero in my bank account is no money(value), but the "empty" space of a bank account. Between the earth and the moon is zero and is space.




Euclid says a dimension is a line ( I agree )

A line is a collection of points ( I agree )

zero is a single point (I agree), with no dimension (I disagree).....



consider.....have you ever seen, or used, a point in mathematics in which the point in question could NOT have be measured? Measurement is a observation involving "space" "dimension"....etc...

If I allow a point to have dimension...it then requires no debate in understanding how a "line" obtains dimension when it is composed of things that do NOT have dimension.....so on.....any better?

[conway]

> > 0 and 1 share identical spaces. ( 1 + (-1) )
> proves
> > this....if 0 did not have a space on the number
> line
> > the equation would equal -1. 0 and 1 do NOT share
> a

> > value in common. 0 is NOT equal to 1. according to

> > value. But according to space they ARE equivalent.
> >

> > 0(as a number) Is NOT = 1(as a number)
> > 0(as value) Is NOT = 1 (as value)
> >
> >
> > 0(as spaces) = 1 (as space)
> >
> > an empty space is still a thing, it is NOT
> > nothing...it can be measured and interacted
> > with......so should zero.
>
> The alleged topmost mathematicians on earth and from
> their moderated or fabricated history had proven long
> ago that (0 = 1), with so many DOCUMENTED references
> that they can't hide, and much more to this they had
> proven rigorously that (p = q), where (p, q) are
> distinct integers, for sure
>
> BKK

BKK


Thanks...I guess?.....but I don't agree with you that infinites are not real....among other things....I will continue to read your post...except the rants(I understand them)....and consider you ideas however.

[conway]

> On Wednesday, September 6, 2017 at 3:01:29 PM UTC-4,
> conway wrote:

> > 0 and 1 share identical spaces. ( 1 + (-1) )
> proves this....if 0 did not have a space on the
> number line the equation would equal -1. 0 and 1 do
> NOT share a value in common. 0 is NOT equal to 1.
>

> Thanks for confirming that, contrary your heading, we
> still have 0=/=1.
>
>

> > according to value. But according to space they
> ARE equivalent.
> >
>

> Huh??? Not sure what kind of wonky equivalence
> relation you have in mind, but it sure isn't
> equality. 0 and 1 are NOT generally interchangeable.
>
> So, we still have 0x=0 and 0x=/=1 for all x in R. And
> 0=/=1. Whew!
>
>
> Dan
>
> Download my DC Proof 2.0 software at
> http://www.dcproof.com
> Visit my Math Blog at
> http://www.dcproof.wordpress.com
>
>
>
>

Dan


To be fair to you....ok....I was not "precise" in my title. I chose it to add "flare".......HOWEVER.....zero and 1 are interchangeable with "space"......but not with value.....

consider..."abstractly"...


If I have an empty box... that is zero. If I fill the empty box with 1 of anything....that is 1. 1 still has the same "box" that zero had....its just that it is "filled"...

[Dan Christensen]

You really need to formalize this system of yours. By this, I mean you need to define everything using purely in the language of predicate logic and maybe set theory. Any inferences you draw should be based not on any spatial intuition as here, but purely on the formal rules of logic as applied to these definition/axioms. You can insert some prose comments about "empty boxes" etc. to help the reader visualize what you are talking about, but they are not to be used in making any logical inferences.


Dan

Download my DC Proof 2.0 software at http://www.dcproof.com <--- CHECK IT OUT!

[Dan Christensen]

This is not merely personal preference, pickiness or pedantry. It really is the "acid test" of your ideas and how they work together. If they cannot be formalized in a way similar to what I have described here, they aren't really mathematics.

[Peter Percival]

conway wrote:


> Euclid says a dimension is a line ( I agree )
>
> A line is a collection of points ( I agree )
>
> zero is a single point (I agree), with no dimension (I disagree).....

Reference?

[William Elliot]

> conway wrote:
>
> > Euclid says a dimension is a line ( I agree )
> > A line is a collection of points ( I agree )
> > zero is a single point (I agree), with no dimension (I
> > disagree).....
>
> Reference?

It has zero dimension. The empty set has -1 dimension.
Reference: Read about Dimension Theory.

[Peter Percival]

Mr, Mrs or Miss Conway mentioned Euclid.

[Markus Klyver]

But zero is a number. How is a number a "dimension"? Do you consider zero-dimensional vector spaces? The only zero-dimensional vector space is the trivial vector space containing the null vector.

Other than that, your babble makes no sense whatsoever. What dimension and what space are you talking about? You are just babbling word salad without any coherent meaning here. EXPLAIN what you mean by dimension and space and EXPLAIN how "zero is a dimension that is empty". And explain how dimensions can be "empty", etc etc.

And a dimension is not a line, and Euclid said no such thing. Please stop being stupid on the Internet, thank you.

[Bill]

I'll help you cut to the chase. It's because that what he does.

[7777777]

keskiviikko 6. syyskuuta 2017 22.01.29 UTC+3 conway kirjoitti:
> 0 and 1 share identical spaces. ( 1 + (-1) ) proves this....if 0 did not have a space on the number line the equation would equal -1. 0 and 1 do NOT share a value in common. 0 is NOT equal to 1. according to value. But according to space they ARE equivalent.

you should take a look at what I wrote here:
https://groups.google.com/d/msg/sci.math/tqTLUyTRdmA/97hBQZmBAQAJ

in my table there is 0 = 1

[conway]

>
> And a dimension is not a line, and Euclid said no
> such thing. Please stop being stupid on the Internet,
> thank you.

Markus


Busted......apologize...admit you were wrong....or cease receiving replies from me.....


https://en.wikipedia.org/wiki/Dimension


here it is again in case you don't like the wiki...


http://www.dictionary.com/browse/dimensions


Id ask you to stop being a troll on the internet...but...that's like asking the sun not to shine.......

Good Luck to you Markus

[conway]

7777777

Thanks! Very Interesting....I'll get back to you...

[Markus Klyver]

I don't see how this supports your case. If we are talking about physical measurements, then 0 has no dimension. If we are talking about some other concept of dimension in mathematics, it has to be more precise. In what way is 0 a dimension???!

[Conway]

markus

if we are talking about physical measurements.....then 0 has a dimension. Can you show me NO dimension. You can not. EVERY where you look there is dimension. If I write zero...it has a dimension. If I draw a dot, it has a dimension. (disregarding Euclid). I do agree however that I should work on more precise definitions.


zero is the least of numbers
numbers represent existence
the least of existence ALWAYS contains a dimension.
zero represents dimension "without a value" inside of it.
A cup that is empty is zero
A cup that is full is the number 1

A line is a dimension that has values(a set of numbers) inside it.
A line that has no values inside it...is zero.

[konyberg]

A point in physics has no dimension (and also in mathematics). It is a singularity.
KON

[Markus Klyver]

A real number has no unit, and is obviously dimensionless. If you are using an other notion of dimension than for physical measurements, you need to define it because otherwise you are not making any sense. And then you go on and claim even more nonsensical and bizarre things. How is a cup the number 1, exactly? How can a line have values? How do numbers represent existence?

You are not making sense and coherence in anything you are saying is lacking.

[Conway]

Kon

considering we do not know what is on the other side of a singularity.....it might then be space. Further...just because I can not measure something because of its smallness or largeness....does not mean it can be measured...

[Conway]

If you can not understand how a line has values...then you are not a human. If you do not understand how numbers represent existence...well clearly you lie here....I have utterly failed to explain my self to you Markus....(also others). In this regard I have nothing else to say to you....unless you something changes on your end....good luck!

[Me]

On Saturday, September 23, 2017 at 2:50:08 AM UTC+2, Conway wrote:

> numbers represent existence...

Especially, if =/= 0. Actually,

Ex(x e M) <-> card(M) =/= 0.

On the other hand, even if we only have

phi(0)

for some "property" phi, we may conclude from this

Ex(phi(x)).

=> Something exists (namely the number 0).

[Conway]

Me

Ok...well said. If then 0 IS something. What then is it? Dimension with out an existence filling it.

[Me]

On Saturday, September 23, 2017 at 3:34:16 PM UTC+2, Conway wrote:

> If 0 IS something. What then is it?

It's a number, a _mathematical_ object.

> Dimension ...

Usually we don't consider numbers to be objects "located" in space-time. Moroever we usually don't assume that they have an extension or a weight or whatever. With other words, no dimension, space, etc. connected just with the number _as such_.

If we have n =/= m for n, m e IN. We do not assume that the two numbers have different "locations", etc. We just assume that the ARE different (not identical) which is a pure "logical" or "mathematical" concept in this case.

What we *do* know (or assume, or deduce) is that there certain mathematical RELATIONS hold between numbers, for examle 0 < 1 < 2, etc.

[Peter Percival]

It's a number. If you want a definition is terms of logically prior
things, then there are various possibilities-
https://en.wikipedia.org/wiki/Natural_number#Modern_definitions

> Dimension
> with out an existence filling it.
>

[Conway]

Me....of course this is well understood....USEUALLY....but usually doesn't mean impossible. Just as you stated...

"we do know, there is certain relations hold between numbers".......come on... that is space....dimension....whatever.....agreed a better definition is needed here. But the "philosophical" logic is there. I might not be able to measure 0, but it has dimension...because it exists on the number line. A line is dimension. It is only that some dimension are beyond our ability to measure.

[Dan Christensen]

If you cannot formally define these concepts of yours purely in terms of the symbols of logic and set theory (or some equivalent), it isn't mathematics. Do your homework if you want to be taken seriously here.

Here again, as an example is a possible formal definition of the set of natural numbers:

1. 0 in N
2. For all x in N: S(x) in N
3. For all x, y in N: [S(x)=S(y) => x=y]
4. For x in N: S(x)=/=0
5. For subsets P of N: [0 in P & For all x in P: [S(x) in P]

From these axioms and the axioms of set theory, we can derive most if not all of modern mathematics. I'm guessing, you will probably want to include these, along some definition of you notion of spaces, dimensions and whatever.

[FredJeffries]

On Saturday, September 23, 2017 at 9:10:59 AM UTC-7, Dan Christensen laid down the law:

> If you cannot formally define these concepts of yours purely in terms of the symbols of logic and set theory (or some equivalent), it isn't mathematics.

That's ridiculous. You have just chauvinistically declared the mathematics of thousands of years and hundreds of cultures to be "n[o]t mathematics"; not to mention all of the experimental and not-yet-formalized current research; not to mention all of the checkbook balancing done by millions of people who never saw a "symbol of logic" in their lives.

[Conway]

Thanks Jeff....Dan is a bit hard to deal with!

[Conway]

Dan

Perhaps you don't remember my reply the last time you posted this table. I thanked you. I also said something to the affect that in no way does the table help. Other than to say the following...

"For all x in N there exists two parts to x"....and so on....

I have also stated that perhaps better definitions for space and value are yet to be achieved. However as Jeff points out....to "some" extent you KNOW what I mean by space and value.....you just don't agree on how I chose to "use" them.....hence the debate. One of which I enjoy....if you don't....well that's on you. At least I'm not a total megalomaniac like some of the "cranks" around here.

[Me]

> to "some" extent you KNOW what I mean by space and value...

Actually, at least *I* don't have the slightes idea what this notions mean in the context of /numbers/ (considered as certain mathematical objects). Moreover, your exposition doesn't seem to be very coherent (to say the least).

> I can "see" the space of zero on ANY number line.

*sigh* It's a mathematical fact: for any two real numbers a and b: if a =/= b, then there is a "distance" between a and b: d := |a - b| > 0, where d is a real number. Hence for any real number a =/= 0, there *is* a distance d := |a| between 0 and a. I guess this is what you are refering to as /space/.

Hint: Mathematical facts do not depend on what "we" can /see/ (or not see). For example, AP can't _see_ that cone sections are ellipses. Still, they are.

[Conway]

Me....point well taken regarding the "see"-ing of mathematics. I understand your cone section are ellipses example perfectly.

Now consider....there is an infinite amount of numbers "between" numbers on the line. If then you agree there is also "space" between these numbers....then we can see how space and value are "interchangeable". One is with-in the other. WE can show how a number is composed of space and of value on all number lines.

[FromTheRafters]

FredJeffries wrote :

Are you saying that all of these thousands of years of mathmematics
later, these things still can not be broken down to formally defined
things "like" sets based on first order logic? I thought this was the
essence of formal mathematical proofs, the ability to 'boil it down' to
the foundational aspects.

I wouldn't say something is not mathematics just because it cannot be
broken down this way, because there are other possible foundations
where some hair-brained scheme might actually work and be provable
under 'some equvalent' theory, as Dan has suggested above.

[Markus Klyver]

Lines are sets of points. How are sets of points values? You are not making sense.

[FredJeffries]

On Saturday, September 23, 2017 at 10:09:44 AM UTC-7, Conway wrote:

> I have also stated that perhaps better definitions for space and value are yet to be achieved. However as Jeff points out....to "some" extent you KNOW what I mean by space and value.....you just don't agree on how I chose to "use" them

I said no such thing.

[FredJeffries]

On Saturday, September 23, 2017 at 10:54:13 AM UTC-7, FromTheRafters wrote:
> FredJeffries wrote :
> > On Saturday, September 23, 2017 at 9:10:59 AM UTC-7, Dan Christensen laid
> > down the law:
> >
> >> If you cannot formally define these concepts of yours purely in terms of the
> >> symbols of logic and set theory (or some equivalent), it isn't mathematics.
> >
> > That's ridiculous. You have just chauvinistically declared the mathematics of
> > thousands of years and hundreds of cultures to be "n[o]t mathematics"; not to
> > mention all of the experimental and not-yet-formalized current research; not
> > to mention all of the checkbook balancing done by millions of people who
> > never saw a "symbol of logic" in their lives.
>
> Are you saying that all of these thousands of years of mathmematics
> later, these things still can not be broken down to formally defined
> things "like" sets based on first order logic?

No, that is not what I said. Neither did I say the contrary. I have no idea how much of mathematics can be so broken down.

> I thought this was the
> essence of formal mathematical proofs, the ability to 'boil it down' to
> the foundational aspects.

There is more to mathematics than "formal mathematical proofs".

Mathematics has been done for thousands of years. The current fad for "defin[ing] ... concepts ... purely in terms of the symbols of logic and set theory (or some equivalent)" has been around for about a century.

I do not deny that it has proved productive in some areas, but it's not all that there is, even now. Two areas that come to mind are fractals and category theory -- neither have the formalistic foundation you require.

[Conway]

My apologies this was FromtheRafters. He/She suggested formal logic was NOT necessarily required to perform mathematics and I agree.

[Dan Christensen]

Ordinary arithmetic (2+2=4, etc.) was formalized some time ago. So too has algebra, calculus, differential equations, etc. As for "experimental" research, it will always be just a preliminary work until it can be axiomatized.

I really have to admire those have staked their careers on such speculative ventures, hacking their way through tractless mathematical jungles, but failure is real possibility. But I guess it wouldn't be very exciting otherwise!

[Dan Christensen]

On Saturday, September 23, 2017 at 1:09:44 PM UTC-4, Conway wrote:
> On Saturday, September 23, 2017 at 11:10:59 AM UTC-5, Dan Christensen wrote:

> >
> > If you cannot formally define these concepts of yours purely in terms of the symbols of logic and set theory (or some equivalent), it isn't mathematics. Do your homework if you want to be taken seriously here.
> >
> > Here again, as an example is a possible formal definition of the set of natural numbers:
> >
> > 1. 0 in N
> > 2. For all x in N: S(x) in N
> > 3. For all x, y in N: [S(x)=S(y) => x=y]
> > 4. For x in N: S(x)=/=0
> > 5. For subsets P of N: [0 in P & For all x in P: [S(x) in P]
> >
> > From these axioms and the axioms of set theory, we can derive most if not all of modern mathematics. I'm guessing, you will probably want to include these, along some definition of you notion of spaces, dimensions and whatever.
> >
> >
> Dan
>

> Perhaps you don't remember my reply the last time you posted this table. I thanked you. I also said something to the affect that in no way does the table help. Other than to say the following...
>
> "For all x in N there exists two parts to x"....and so on....
>

So, is x an ordered pair of objects or what? You will have be more specific.

> I have also stated that perhaps better definitions for space and value are yet to be achieved.

You've tested the waters for your ideas here and the reaction must be discouraging for you, but you now have to decide how much time and effort you want to spend on this division-by-zero project. Either quit, or get on with the next phase of your project and come up with something more concrete.

> However as Jeff points out....to "some" extent you KNOW what I mean by space and value.....

I'm not just playing the silly bugger to trip you up on minor details like some pedants here are wont to do. I really have no clue what you are talking about.

[Conway]

Dan

Thanks for you time. I have learned from you. I shall continue as I have.

[Peter Percival]

Dan Christensen wrote:
> On Saturday, September 23, 2017 at 12:41:43 PM UTC-4, FredJeffries
> wrote:
>> On Saturday, September 23, 2017 at 9:10:59 AM UTC-7, Dan
>> Christensen laid down the law:
>>
>>> If you cannot formally define these concepts of yours purely in
>>> terms of the symbols of logic and set theory (or some
>>> equivalent), it isn't mathematics.
>>
>> That's ridiculous. You have just chauvinistically declared the
>> mathematics of thousands of years and hundreds of cultures to be
>> "n[o]t mathematics"; not to mention all of the experimental and
>> not-yet-formalized current research; not to mention all of the
>> checkbook balancing done by millions of people who never saw a
>> "symbol of logic" in their lives.
>
> Ordinary arithmetic (2+2=4, etc.) was formalized some time ago. So
> too has algebra, calculus, differential equations, etc. As for

Where have differential equations (a hell of a big subject!) been
formalized...

> "experimental" research, it will always be just a preliminary work
> until it can be axiomatized.

... in the sense of axiomatized? Indeed, what would it mean "to
formalize" differential equations? That an equation and some axioms are
put into a box, shaken well, and out pop the solutions?

> I really have to admire those have staked their careers on such
> speculative ventures, hacking their way through tractless
> mathematical jungles, but failure is real possibility. But I guess it
> wouldn't be very exciting otherwise!
>
>
> Dan
>
> Download my DC Proof 2.0 software at http://www.dcproof.com Visit my
> Math Blog at http://www.dcproof.wordpress.com
>

[Conway]

Peter well said. Not to mention that an AXIOM by definition can NOT be proven. It is by definition a self inherent truth. I mean...numbers are composed of space and value is a self inherent truth. There is no way to prove this. Such as there is no way to prove the multiplicative identity of property of zero...it just is......yet Dan cant seem to function without linear formal logic....I almost think he is a bot.

[Peter Percival]

Conway wrote:
> [...] I mean...numbers are composed of space and value is a self
> inherent truth.

But no one believe it other than you.

> There is no way to prove this. Such as there is no
> way to prove the multiplicative identity of property of zero...it
> just is......yet Dan cant seem to function without linear formal
> logic....I almost thinkhe is a bot.
>

[Dan Christensen]

On Sunday, September 24, 2017 at 8:19:14 AM UTC-4, Peter Percival wrote:
> Dan Christensen wrote:
> > On Saturday, September 23, 2017 at 12:41:43 PM UTC-4, FredJeffries
> > wrote:
> >> On Saturday, September 23, 2017 at 9:10:59 AM UTC-7, Dan
> >> Christensen laid down the law:
> >>
> >>> If you cannot formally define these concepts of yours purely in
> >>> terms of the symbols of logic and set theory (or some
> >>> equivalent), it isn't mathematics.
> >>
> >> That's ridiculous. You have just chauvinistically declared the
> >> mathematics of thousands of years and hundreds of cultures to be
> >> "n[o]t mathematics"; not to mention all of the experimental and
> >> not-yet-formalized current research; not to mention all of the
> >> checkbook balancing done by millions of people who never saw a
> >> "symbol of logic" in their lives.
> >
> > Ordinary arithmetic (2+2=4, etc.) was formalized some time ago. So
> > too has algebra, calculus, differential equations, etc. As for
>
> Where have differential equations (a hell of a big subject!) been
> formalized...
>

Don't know a good reference off hand.

> > "experimental" research, it will always be just a preliminary work
> > until it can be axiomatized.
>
> ... in the sense of axiomatized? Indeed, what would it mean "to
> formalize" differential equations? That an equation and some axioms are
> put into a box, shaken well, and out pop the solutions?
>

If "shake well" includes repeatedly invoking specific rules of logic and axioms of set theory, then yes.

[Conway]

Yes, yes....captain obvious....well said again.....maybe one day....probability however not in my favor.

[Dan Christensen]

You mean, you will just keep repeating your half-baked ideas as they are and hope you will amass a huge international following without having to work out the details?

As a cautionary tale, take a good look at the online careers of math failures JG, AP and WM spanning decades here and at other forums. That strategy has not worked for them. (Not suggesting you are anywhere near as toxic as JG.)

You yourself have conceded that your "definitions" need some work. Do it. And apply them to at least one important theorem. You are wasting your time here otherwise.

[Dan Christensen]

Important? OK, that may be a bit much. How about just the functionality, associativity, commutativity and cancelability of addition and multiplication on this set of 2-part numbers of yours?

[FredJeffries]

On Sunday, September 24, 2017 at 9:37:09 AM UTC-7, Dan Christensen wrote:

> As a cautionary tale, take a good look at the online careers of math failures JG, AP and WM spanning decades here and at other forums. That strategy has not worked for them.

On the contrary, it has worked beautifully for them. And you. Thirty of so years ago they would have been unable even to present their message unless they were wealthy enough to own (or bribe) a printing company.

Now, every one of their silliest thoughts is read and commented on by at least one other person (i.e. you) and propagates like a virus through the world wide web via comments and comments on the comments and comments on the....

You are the best friend these posters have ever had.

[FredJeffries]

On Sunday, September 24, 2017 at 7:47:27 AM UTC-7, Conway wrote:

> [A]n AXIOM by definition can NOT be proven. It is by definition a self inherent truth.

No. In mathematics an axiom is merely a working hypotheses, a "mathematical statement that serves as a starting point from which other statements are logically derived."
https://en.wikipedia.org/wiki/Axiom

Any coherent mathematical statement (or it's converse) may be taken as an axiom. Of course, having "made it happen", you must then honestly "deal with the consequences", per James Tanton
http://gdaymath.com/about/

As I see it, YOU have two problems. You haven't been able to express your ideas coherently (and lash out at anyone and everyone making an attempt to clarify), and you aren't willing to deal with the (mathematical) consequences-- for instance, that if you can divide by 0 then you haven't got a field.

[Dan Christensen]

Hear that trolls? I am your best friend! It's better to be exposed as frauds and publicly ridiculed than to be ignored, right? Better 1 chance in a million of than 0 chances. (Hee, hee!)

[Me]

On Sunday, September 24, 2017 at 8:29:43 PM UTC+2, Dan Christensen wrote:
> On Sunday, September 24, 2017 at 2:05:51 PM UTC-4, FredJeffries wrote:
> >
> > You are the best friend these posters have ever had.
> >
> Hear that trolls? I am your best friend! It's better to be exposed as frauds
> and publicly ridiculed than to be ignored, right? Better 1 chance in a million
> of than 0 chances. (Hee, hee!)

And, of course, *he* never replies to troll posts.

[Conway]

Your second link proves my statement about axioms. I have dealt with the fact. If you understood what I wrought in my axiom you would have understood you CAN have a field. Multiplication by zero (under my idea) works like it currently does now...as well as like multiplication by 1....both EXIST in CURRENT fileds.....it is you who is lashing out....clearly.....you are also the best friend of trolls...as evidenced by your reply to Dan....and continued replies to me in violation of your own rule (HE HE)....

[Conway]

All properties..."axioms" in field theory STAY the same...I have said this. All it takes is to add to them....mine. That is to say commutative, associative, distributive....additive and so on....do NOT change.....

[Dan Christensen]

On Sunday, September 24, 2017 at 2:49:24 PM UTC-4, Conway wrote:

>
> All properties..."axioms" in field theory STAY the same...I have said this. All it takes is to add to them....mine. That is to say commutative, associative, distributive....additive and so on....do NOT change.....

Hmmm... The field axioms tell us that that 0x=0 for all x in R and 0=/=1. Therefore there is no solution to 0x=1. You claim there is. Some or all of the fields axioms will have to go in your system, Conway. Or maybe you can think of some clever work-around. ;^)

[Conway]

Dan


Yes!......that is exactly what I "think" I have done. A "clever work around". So then if you really wish to challenge the "kookery" of my idea...as opposed to personal insults...then do me a favor here.

Assume the "axiom" I gave is valid.

Now find a violation in ANY of these field axioms.....
http://mathworld.wolfram.com/FieldAxioms.html


Hint...there isn't any. I have had this idea in front of many PHD's. They all agree there is no flaw in the math. It is ONLY a matter of convincing others that the axiom I gave is actually a self inherent truth.....lol....there in lies the problem as you and others have pointed out.

[Dan Christensen]

On Sunday, September 24, 2017 at 4:09:03 PM UTC-4, Conway wrote:
> On Sunday, September 24, 2017 at 2:46:49 PM UTC-5, Dan Christensen wrote:
> > On Sunday, September 24, 2017 at 2:49:24 PM UTC-4, Conway wrote:
> >
> > >
> > > All properties..."axioms" in field theory STAY the same...I have said this. All it takes is to add to them....mine. That is to say commutative, associative, distributive....additive and so on....do NOT change.....
> >
> > Hmmm... The field axioms tell us that that 0x=0 for all x in R and 0=/=1. Therefore there is no solution to 0x=1. You claim there is. Some or all of the fields axioms will have to go in your system, Conway. Or maybe you can think of some clever work-around. ;^)
> >
> >
> > Dan
> >
> > Download my DC Proof 2.0 software at http://www.dcproof.com
> > Visit my Math Blog at http://www.dcproof.wordpress.com
>
> Dan
>
>
> Yes!......that is exactly what I "think" I have done. A "clever work around". So then if you really wish to challenge the "kookery" of my idea...as opposed to personal insults...then do me a favor here.
>
> Assume the "axiom" I gave is valid.
>

So, you now agree that 0x=1 has no solution. Now we are getting somewhere!

[FredJeffries]

Of course I do. (I respond to you, don't I?)

I even admit to doing an occasional troll myself.

For anyone who might be interested (I am sorry for you), the snipped issue I was actually responding to was:

>As a cautionary tale, take a good look at the online careers of math failures JG, AP and WM spanning decades here and at other forums. That strategy has not worked for them.

https://groups.google.com/forum/#!original/sci.math/DX1MHQORoHA/nBLn_87pAAAJ

[Me]

On Sunday, September 24, 2017 at 10:29:06 PM UTC+2, FredJeffries wrote:

> I even admit to doing an occasional troll myself.

Shame on you! :-)

> For anyone who might be interested (I am sorry for you), the snipped issue
> I was actually responding to was:
>
> > As a cautionary tale, take a good look at the online careers of math
> > failures JG, AP and WM spanning decades here and at other forums. That
> > strategy has not worked for them.

That's certainly the case.

[Conway]

I'm not sure how you made that jump. I do believe there is a solution to 0x=1. Further I believe you can find the solution without losing ANY of the axioms I linked to. Only adding one axiom provides the solution.

[Dan Christensen]

On Sunday, September 24, 2017 at 4:33:33 PM UTC-4, Conway wrote:
> On Sunday, September 24, 2017 at 3:16:32 PM UTC-5, Dan Christensen wrote:
> > On Sunday, September 24, 2017 at 4:09:03 PM UTC-4, Conway wrote:
> > > On Sunday, September 24, 2017 at 2:46:49 PM UTC-5, Dan Christensen wrote:
> > > > On Sunday, September 24, 2017 at 2:49:24 PM UTC-4, Conway wrote:
> > > >
> > > > >
> > > > > All properties..."axioms" in field theory STAY the same...I have said this. All it takes is to add to them....mine. That is to say commutative, associative, distributive....additive and so on....do NOT change.....
> > > >
> > > > Hmmm... The field axioms tell us that that 0x=0 for all x in R and 0=/=1. Therefore there is no solution to 0x=1. You claim there is. Some or all of the fields axioms will have to go in your system, Conway. Or maybe you can think of some clever work-around. ;^)
> > > >
> > > >
> > > Dan
> > >
> > >

> > > Yes!......that is exactly what I "think" I have done. A "clever work around". So then if you really wish to challenge the "kookery" of my idea...as opposed to personal insults...then do me a favor here.
> > >
> > > Assume the "axiom" I gave is valid.
> > >
> >
> > So, you now agree that 0x=1 has no solution. Now we are getting somewhere!
> >
>

> I'm not sure how you made that jump. I do believe there is a solution to 0x=1.

Nope. From the field axioms, it can be shown that 0x=0 for all x in R. (Nice little exercise.) We also have 0=/=1. Something's got to give here.

[Conway]

Ok Dan....Allow me to try again. Here it is in pure math. No words like "space" or "value" involved.....PURE math...

Axiom

Let every number be arbitrarily composed of two numbers.

Let the number table exist as such…

0=(0,1)
1=(1,1)
2=(2,2)
3=(3,3)
4=(4,4)…and so on

Let the first number of the number chosen be labeled as z1

Let the second number of the number chosen be labeled as z2

Let multiplication exist as follows…

(A x B) = ( z1forA x z2forB ) = ( z2forA x z1forB ) = ( z1forB x z2forA ) = ( z2forB x z1forA )

Let division exist as follows…

(A/B) = ( z1forA/z2forB )
(B/A) = ( z1forB/z2forA )

[FredJeffries]

On Sunday, September 24, 2017 at 4:40:01 PM UTC-7, Dan Christensen wrote:

> From the field axioms, it can be shown that 0x=0 for all x in R. (Nice little exercise.) We also have 0=/=1. Something's got to give here.

Usually distributivity is the first casualty, since

1 = 0x = (0 + 0)x =? 0x + 0x = 1 + 1

[Conway]

Using the afore mentioned axiom. Let x = 1

1 = 0(1) = (0 + 0 )1 = 1 0(1) + 0(1) = 1 + 1


*if and only if I use z2 for 0....z2 for 0 is 1...therefore it acts like multiplication by 1...but is actually 0*