Date: Nov 20, 2012 4:09 AM
Author: Graham Cooper
Subject: SET THEORY  and   QUANTIFIER LOGIC  are  SUPERFLUOUS!  You only need<br> 1 or the other!

The notation in

{ x | p(x) }

stands for ALL VALUES OF x
that are satisfied in p(x)

This is the SAME 'ALL' as ALL(x) ....predicate(..predicate...
x ...) ...)

ALL is merely SUBSET!

ALL(n):N n+1 > n

is just

{ n | neN } C { n | n+1>n }

----------------------

ALL(x):N xeR

is just

{ x | xeN } C { x | xeR }

Naturals are a subset of Reals!

All Naturals are elements of Reals!
A(x):N xeR

--------------------

This is good news for me since I'm adding breadth first functionality
to microPROLOG (sets of results) so I just have to figure out a set
notation with { }.

e.g.
union( { 1 2 3 } , { 3 4 } , X }

X = { 1 2 3 4 }

So I can avoid the horrors of eliminating quantifiers by making you
write the theorems in set theory notation instead! Haha!

Herc

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