
SET THEORY and QUANTIFIER LOGIC are SUPERFLUOUS! You only need 1 or the other!
Posted:
Nov 20, 2012 4:09 AM


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
 www.microPROLOG.com if( if(t(S),f(R)) , if(t(R),f(S)) ). if it's sunny then it's not raining ergo if it's raining then it's not sunny

