Date: Nov 17, 2012 9:30 PM
Author: INFINITY POWER
Subject: wikipedia.org/wiki/Quantifier#Equivalent_Expressions

http://en.wikipedia.org/wiki/Quantifier#Equivalent_Expressions

AxeX P(x)
/\
||
\/
{xeX} -> P(x)

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

THIS IS JUST ABSOLUTELY INCREDIBLE!

NOBODY EVERY REALISED ALL(X) is just SubSet!

AxeX P(x)
/\
||
\/
{x|xeX} C {x|P(x)}

ALL SOLUTIONS FOR X in LHS SET
is a subset of
ALL SOLUTIONS FOR X in RHS SET


ALL(x)...
is the same PARAMETER NAMING SYSTEM AS
{ x | .... }

ALL(x):N P(x)
is just
{ x | xeN } C p(x)

ALL x satisfying xeN

SAME ALL!

The real reason SET THEORY embeds logic, when they're actually 2 different
SYNTAXES for ALL(x).

And another of my 100 Proofs Of Logic totally ignored by all sci.logic,
sci.math.

Herc
--
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