Date: Nov 15, 2012 1:44 AM
Author: Hercules ofZeus
Subject: Re: ALL(F):N->R is 2OL! NOT 1OL!!!!!!
On Nov 15, 4:24 pm, forbisga...@gmail.com wrote:

> ALL(A)[(EXISTS(w)(weA) AND EXISTS(x) ALL(w)(weA->w<=z))->

> EXISTS(x) ALL(y)([All(w)(weA->w<=y)]<->x<=y)]

>

> where <= is being used as "less than or equal to".

> I'm leaving the brackets in place because it appears

> some use it as a transform from true to 1 and false to 0.

> I dont get it in this context. It seems to mix some

> programming languages' coding for the comparison operators

> with their logical value.

>

Most people here use A(x) E(x) or Ax Ex

I *emphasised* ALL(F):

merely to imply the reading "ALL FUNCTIONS", since that was my point

about 2OL.

<= is definable using Peano Arithmetic

A(n) 0 <= n

A(m) A(n) s(m)<=s(n) -> m<=n

e.g.

s(0) <= s(s((0)) ?

m=0 n=s(0)

s(m)<=s(n) -> m<=n 2nd Axiom

0 <= s(0) 1st Axiom

Herc