```Date: Nov 25, 2012 8:01 PM
Author: Graham Cooper
Subject: Re: On Generalizing the Natural Numbers

On Nov 26, 3:37 am, George Greene <gree...@email.unc.edu> wrote:> On Nov 24, 6:59 pm, Charlie-Boo <shymath...@gmail.com> wrote:>> > Define ADD(a,b,c) as a+b=c>> That is not doable unless you ALREADY defined "+" and "=".> HOW DID YOU DO *THAT*??>> > and MUL(a,b,c) as a x b = c (Peano's axioms.)>> If I already have Peano's Axioms then why am I not simply ALREADY> FINISHED?> WHY DO I NEED *YOUR* upper-case predicates AS WELL??> Don't you know you could just REWRITE Peano's Axioms USING your> upper-case predicates?  Isn't that what you REALLY MEANT to do?>> ADD( x,0, x) ?> MUL( x,1, x) ?>> > For any relation P(,) defind P(I,x) as the> > process of inputting a value for I and outputting all values for x> > that are in that relation, where I in general is any number of> > components with values I, J, K, . .. and x is x, y, z, ...  That is,> > R(I,x) = { x | R(I,x) is true.}>> What in THE HELL makes you think any of THAT shit is COHERENT??> You CANNOT HAVE> R(I,x) = { SOME SET }> AND THEN *SIMULTANEOUSLY* HAVE (as you have inside on the right of the> set-brackets)> "R(I,x) is true"!!  R(I,x) CANNOT simultaneously be BOTH *a*SET* AND a> TRUTH-value!!>It's workable though.  Certain predicates, let's give them aconvention of starting with s,sadd( n,m,a )is the set of all values of a that satisfy n+m=aNow at the HUMAN/COMPUTER PARSER LEVEL, we convert this to and from:{a | add(n,m)=a }or just  {a | sadd(n,m,a) }     //for those of us who use prefixfunctionse.g.E(n) n=4E(m) m<=3{a | add(n,m)=a }and the PROLOG PREPARSER converts this to:?- sadd(4,M,A) , less(M,3)outputs the full result setM=0,  A=4M=1,  A=5M=2,  A=6M=3,  A=7then the PROLOG POSTPARSER converts it back to the Human Format{ 4, 5, 6, 7 }*************I think  pred(X, a, b, c)   <=>  { X | pred(X, a, b, c) }might be a more natural convention, X is argument 1.Herc
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