
Re: On Generalizing the Natural Numbers
Posted:
Nov 25, 2012 8:01 PM


On Nov 26, 3:37 am, George Greene <gree...@email.unc.edu> wrote: > On Nov 24, 6:59 pm, CharlieBoo <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* uppercase predicates AS WELL?? > Don't you know you could just REWRITE Peano's Axioms USING your > uppercase 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 > setbrackets) > "R(I,x) is true"!! R(I,x) CANNOT simultaneously be BOTH *a*SET* AND a > TRUTHvalue!! >
It's workable though. Certain predicates, let's give them a convention of starting with s,
sadd( n,m,a )
is the set of all values of a that satisfy n+m=a
Now 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 prefix functions
e.g.
E(n) n=4 E(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 set
M=0, A=4 M=1, A=5 M=2, A=6 M=3, A=7
then 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

