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.

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

        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.

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.

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

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

0 is not "nothing" it's 0.

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


Dan

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?

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

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.....

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.

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

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

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.

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....

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?

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

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.

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.

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.

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

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.

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.
>

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.

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.


>
> 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.
>>
>
>

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

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.

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

>
>
> 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.....

> 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.

> 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

>
> 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.

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

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

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?

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"...

> > 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.

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!

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.

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?

> 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.

Mr, Mrs or Miss Conway mentioned Euclid.

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.

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

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

>
> 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

7777777

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

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???!

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.

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

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.

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...

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!

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).

Me

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

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.

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.
>

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.

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.

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.

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

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.

> 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.

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.

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.

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

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.

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.

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

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!

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.

Dan

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

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
>

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.

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.
>

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.

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

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.

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?

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.

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.

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!)

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.

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)....

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.....

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.  

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.

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!

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

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.

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.

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.

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 )

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

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*

On Sunday, September 24, 2017 at 8:09:05 PM UTC-4, Conway wrote:

> 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 )

See my reply in your "New Axiom" thread.


Dan

On Sunday, September 24, 2017 at 8:09:05 PM UTC-4, Conway wrote:

> > > > 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.
> >

But wait! You didn't address this point. Have you decided to drop the field axioms?

I decided to start a new post not using words like space and value.  I was hoping you would then see that the equation you expressed is true under this axiom.  It is possible however to "take" a different path.....see the revised axiom

conway wrote:
>> 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.
>
Yes, but, not only aren't numbers what you can see (or even "see"), but
they don't constitute lines either.  The one-one correspondence between
numbers and points on a line is a postulate of the arithmetization of
Euclidean (for example) geometry.  In finite geometries and non-metric
geometries there is no such one-one correspondence.

conway used his keyboard to write :

>> 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.

This reminds me of a story my father once told me. One time he said he
was shopping for groceries in the little store we frequented. A man
comes in and says he is moving and asks the proprietor if he has any
empty boxes he can have. The store owner asks him "Empty boxes of
what?"

Yes, but, SPACE is what you can see and measure.  SPACE does constitute a line. Which Is what I claimed.  Why dreg this up....?  I know your thoughts in this regard Peter.

Well said....an empty box is still something. We can show how one empty box has something different in it as compared to another.  It is impossible for anyone to have or represent nothing......go ahead try...you will always have something....just not the thing in question.....

It happens that Conway Lovett formulated :
I thought that you would like that anecdote.

Conway Lovett wrote:
> On Wednesday, October 4, 2017 at 5:37:16 AM UTC-5, Peter Percival
> wrote:
>> conway wrote:
>>>> 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.
>>>
>> Yes, but, not only aren't numbers what you can see (or even "see"),
>> but they don't constitute lines either.  The one-one correspondence
>> between numbers and points on a line is a postulate of the
>> arithmetization of Euclidean (for example) geometry.  In finite
>> geometries and non-metric geometries there is no such one-one
>> correspondence.


>

> Yes, but, SPACE is what you can see and measure.  SPACE does

What has what one can see got to do with any theory of real numbers?

> constitute a line. Which Is what I claimed.  Why dreg this up....?  I
> know your thoughts in this regard Peter.
>

Peter Percival presented the following explanation :
That's a good story too.

Peter...

It is my opinion/axiom that all numbers are composed of space and value.  Hence that specific debate involving space. Nor did my claim rest soley on "What I can see"...i also gave an equation expressing the "space" of zero.

Consider that an atheist is not absent beleif...therefore they are not absent relegion...only absent in beliefs and relegion concerning god.

Conway Lovett wrote:
> Peter...
>
> It is my opinion/axiom that all numbers are composed of space and
> value.

Value I understand (though I don't know if my understanding is the same
as yours), but but space in connection with numbers I don't get.

>  Hence that specific debate involving space. Nor did my claim
> rest soley on "What I can see"...i also gave an equation expressing
> the "space" of zero.
>
> Consider that an atheist is not absent beleif...therefore they are
> not absent relegion...only absent in beliefs and relegion concerning
> god.
>

Peter...

Consider the followig....

Show me a lack of space....

Anywhere and anyhow that you may...

You can not....

Space is everywhere...

Everything occupies space...includeing numbers


This is best visualized with a number line.

Again consider the number line relative to the expression 0 + (-1)

I can not reply with a quote from a cell...sorry

Conway Lovett wrote:
> Peter...
>
> Consider the followig....
>
> Show me a lack of space....
>
> Anywhere and anyhow that you may...
>
> You can not....
>
> Space is everywhere...
>
> Everything occupies space...includeing numbers

Concrete things occupy space.  Numbers are abstractions.

>
>
> This is best visualized with a number line.
>
> Again consider the number line relative to the expression 0 + (-1)
>
> I can not reply with a quote from a cell...sorry
>

All abstractions contain space. I can not imagine a unicorn without my neurons firing. The length of the neurons firing is the length of the abstraction of a unicorn

Suppose you are right about abstraction not having space.  If and when a number is used to represent a thing...then the number must represent the totality of the thing in question...which includes space.

Lastly...you can not represent any kind of abstraction...number or otherwise without makeing use of space...go ahead try....

Conway Lovett wrote:
> All abstractions contain space. I can not imagine a unicorn without
> my neurons firing. The length of the neurons firing is the length of
> the abstraction of a unicorn

What a load of bollocks!

On Wednesday, October 4, 2017 at 2:54:30 PM UTC-4, Conway Lovett wrote:
> All abstractions contain space. I can not imagine a unicorn without my neurons firing. The length of the neurons firing is the length of the abstraction of a unicorn
>

Another idiocy for the ages!


Dan

Peter

Correct me here if I'm wrong...

This thread was over a week old with no replys...

Why did you bring it back up if nothing had changed in your opinion?


Only two scenarios exist...

1.  Your just a troll
2.  Something I said is nagging the back of your mind....saying...he may just be right.

You have given no coherent account of how a number consists of both
space and value.  Also, can you please learn how to post to Usenet?

Peter

 I have given a coherent defention...just not in your's or dan' s opnion....among others...you need to let it go or figure out what it is I'm trying to tell you.

Also I can NOT post with a quote from a phone....I have told you this...read the entirety of my post or don't bother

And you post in a math newsgroup because ???

Bill...

It was relevant to the discussion at hand.  Read the OP and the post that follow if you wish to see how we got from there to here.......if you take issue with the sort of material posted here....you'll find far more offensive material requiring your attention.

You might as well go on with your constructions
not receiving much shall we say constructive,
criticism.

Though, you can readily expect others to understand
their constructive content.

Ross...

Well said...and I agree...

Ross A. Finlayson used his keyboard to write :
I have not been fighting the idea, but it is my belief that he is
trying to 'get around' some perceived problem with zero -- it being
excluded from being a denominator. I feel that the so-called problem
has already been solved via the Limit idea.

Ingrained in my mind is the idea that numbers are values devoid of any
other thing such as he suggests like 'space'. The reason is by the
surprising (to me at the time) idea that the rationals are not
continuous. It would seem that due to the fact that denominators can be
any natural number, perhaps infinitely large, that the 'distance' (or
space?) between adjacent ones on the rational number line could be
completely filled. Their being 'discreet' values had escaped me at the
time.

Then there are irrational numbers arrived at by algebra (such as the
squareroot of two) which must 'fit' between some two of these
previously determined rational numbers. Okay, so that surely must fill
the line up. These irrationals are algebraic and are countable. Then
there are the transcendentals, and again there must be "room" for them.
Uncountably many of them. I think that there must be no "width" to
numbers at all on the real number line.

So bottom line:

1) If it ain't broke, don't fix it.
2) That doesn't mean such an idea is meaningless, in fact new math is
often created while exploring things which for all intents and purposes
*seem* meaningless to others at the time they are being explored.
Euler's Totient function comes to mind here, I read somewhere that it
was considered 'a neat trick, but what good is it' by other
mathematicians of the time. It turns out to be quite useful today in
simplifying calculations reducing the 'computing cost' of encryption
related calculations.

Ross

I feel your post makes my point. I do not say this sarcastically or rudely....as you say


"there MUST be ROOM for them all......"

you however say...therefore this means numbers have NO space

I however say... this means space and value are "interchangeable"...or "relative"


"if it ain't broke don't fix it"...I agree

but this does NOT mean

"if it ain't broke don't improve upon it"

there is always room for improvement

as you say

this all might seem pointless now...but later.....

Conway pretended :
I'm not Ross, I was replying to Ross. I agree with Ross about you not
being discouraged in your explorations just because of a lack of
constructive criticism.

This is Ross.  

I'd carry on with your alternating systems about numbers
then where you can define a notation to reflect the results,
about later having something like "equals"
having been overloaded or "0 not equals 1".

So when you describe these value spaces and comment on
their properties it's pretty much always with a rather
limited, direct, expressive, and correct name and notation
in "mathematics" that it already has all its names just
from what it is.

That's not to say that anybody's paying attention,
even though they might and have constructive criticism
(or often and usually references to existing work).

Anyways the structures have all their content then
for example 0 to 1 etcetera.

It's how they do not that they don't, then for where
your definitions are sound when they fit with all your
other definitions.

เมื่อ วันพฤหัสบดีที่ 5 ตุลาคม ค.ศ. 2017 12 นาฬิกา 25 นาที 29 วินาที UTC+7, Ross A. Finlayson เขียนว่า:
ความศานติและความเอ็นดูเมตตาและความโปรดปรานของอัลลอฮฺ  
develop points if math today not works????????????
https://www.facebook.com/photo.php?fbid=882905925197733&set=pcb.882906115197714&type=3&theater

Ross A. Finlayson explained on 10/5/2017 :
Hello Ross. This is who you replied to, and I have no such system being
as I am comfortable with the systems we already have. Perhaps you meant
to reply to Conway? He is the one with the duality of zero thing where
zero's value can be chosen from amongst [1:0] to avoid a problem with
denominators.

> I'd carry on with your alternating systems about numbers
> then where you can define a notation to reflect the results,
> about later having something like "equals"
> having been overloaded or "0 not equals 1".

Choosing a numerical value of one for zero when it is in a denominator
only makes more trouble IMO. A value infinitesimally short of infinity
suddenly becomes one. If you started with 1/epsilon when epsilon is
'close' to zero (very big number) and gets switched to a one if the
epsilon disappears (becomes actually zero) big discontinuity at the
point of switching.

Better would be to take hints from the neighborhood around zero like
the current standard system does with limits.

> So when you describe these value spaces and comment on
> their properties it's pretty much always with a rather
> limited, direct, expressive, and correct name and notation
> in "mathematics" that it already has all its names just
> from what it is.

Something is lost in translation here.

> That's not to say that anybody's paying attention,
> even though they might and have constructive criticism
> (or often and usually references to existing work).
>
> Anyways the structures have all their content then
> for example 0 to 1 etcetera.
>
> It's how they do not that they don't, then for where
> your definitions are sound when they fit with all your
> other definitions.

Yeah, you completely lost me there.

Anyway, I'm sure Conway will read your post despite it being a reply to
me.

Ross

I have done this in another post

Let zero have the multiplicative property of zero
Let zero have the multiplicative identity property of 1

and so on......

no "table" or "equal" signs necessary....should you like I will post it here again

Rafters...

I apologize (again) for mis quoting you....

I have NEVER claimed that you can chose z1 or z2 in denominators

I claimed the exact opposite...in division

The numerator must be z1 the divisor must be z2

Math today does work, but there is more than that, that
also does work, finding more relations in structures that
produce and reduce systems of equations.

I think SL's diagrams and points are interesting, but it
is the formal presentation (presentation in forms) that
is the development.

Then, about the number theory and the real analysis and
geometry and as about the primes and other fundamental
objects, it's amazing that they're all one mathematics.
Finding fundamental and extended relations is the course.

That's where it seems you have an extension via the properties
of numbers, that then you've overloaded the notation with the
principal notations of the numbers, where instead you can
make your own notation to disambiguate from the "usual"
numbers and your own definition, so that it's sound to
both your development (the properties you establish of
the relations of the objects of the development) and "the"
development (all the properties established as the relations
of all the objects of the overall development).

So, it was mostly a comment on the strength of notation
and its requirements, with the same for all (as mathematics'
objects are enduring and same for all).

Ross

I understand that presentation is everything.  I have written 3 versions.  One with a number table...in case the original with definitions of space and value doesn't work.  And one with properties and instructions on use...in case the number table and it's equivalency gives issue.  I am of course still falling short here.  

Lastly...

A number being "overloaded" with properties is a null argument.  I can assign a million properties to ONE number if I want.  So long as the properties do NOT yield contradictions.  So then if you really want to help....look for them...I have... and have not found any.....(probability is this is do to my ignorance).

So...

As long as we can accept axiomatically....numbers have two composites

As long as we can show a unique sum or sums for A * 0 without contradiction

Then the idea is valid......trouble with presentation or not......

Den fredag 22 september 2017 kl. 04:20:06 UTC+2 skrev conway:
> > 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/9
> > 7hBQZmBAQAJ
> >
> > in my table there is 0 = 1
> >
>
> 7777777
>
> Thanks! Very Interesting....I'll get back to you...

If you agree with him, you need to reevaluate as he is always wrong.

Zelos

No one is ALWAYS wrong.  Even fools have some wisdom...if you know how to listen.  Further...I think 7777777 is wrong...sorta..but in the same way that I found an interesting correlation between 0 and 1 so did he/she....but 0 =/= 1....in his or my post...atleast not entirely...

What was thr point of your reply? Just to be mean?

But for the fools of mathematics, zero, and one are all the same as long as it is only a mind game, and never related to any reality, plus heaven to live in with stars and away from any noise

 Now, the internet is invaded by this puzzle with many videos, articles, topics, that are making the greatest fun of mathematicians all over the world, where not a single research paper in mathematics had been there

 The good one that one video proving that (1 = 0), and people are truly and slowly discovering how stupids the mathematicians are indeed

Beyond human normal imaginations. FOR SURE

But the public still don't know all the other very bad traits that mathematicians truly enjoy generally from birth

BKK

   

they are not the same you moron