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wikipedia.org/wiki/Quantifier#Equivalent_Expressions
Posted:
Nov 17, 2012 9:30 PM
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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)
/\
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\/
{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
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