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Topic: ALL(F):N->R is 2OL! NOT 1OL!!!!!!
Replies: 6   Last Post: Nov 15, 2012 2:39 AM

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Hercules ofZeus

Posts: 27
Registered: 9/19/11
Re: ALL(F):N->R is 2OL! NOT 1OL!!!!!!
Posted: Nov 15, 2012 1:44 AM
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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



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