```Date: Sep 23, 2017 1:09 PM
Author: Conway
Subject: Re: 0 = 1

On Saturday, September 23, 2017 at 11:10:59 AM UTC-5, Dan Christensen wrote:> On Saturday, September 23, 2017 at 11:37:56 AM UTC-4, Conway wrote:> > On Saturday, September 23, 2017 at 9:13:48 AM UTC-5, Me wrote:> > > 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.> > > > 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.> > Dan> > Download my DC Proof 2.0 software at http://www.dcproof.com> Visit my Math Blog at http://www.dcproof.wordpress.com> > > Dan> > Download my DC Proof 2.0 software at http://www.dcproof.com> Visit my Math Blog at http://www.dcproof.wordpress.comDanPerhaps 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.
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