CANTORS MISSING SET FORMULA IS A *JOKE* !!!

[Graham Cooper]

> Zermelo's "Z" set theory proves that the set of all subsets of N (i.e.
> the power set of N) is uncountable, but it doesn't state that all
> those subsets of N are definable in a parameter free manner,


This is in direct opposition to Naive Set Theory where

EVERY MEMBER OF EVERY SET is DEFINABLE BY A PREDICATE

So Axiom Of Choice was added :

A CHARACTERISTIC ELEMENT DEFINES A SET.

e.g.
midpoint( L : LINE )
if a midpoint exists, then so does a line!

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

Or in Cantor's Case:
if an Anti-Diagonal Exists, then so does a SET OF THOSE REALS!

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

AOC: E(X) XeS -> E(S)

If 1 element is definable then so is the set.

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

But A.O.C. only complicates matters further...

It seems to define uncountable many elements
with a specification of 1 element <=> 1 set.

THE GODEL NUMBER OF A CHOICE FUNCTION

2 1 3 0 4 1 5
a 1 ( 0 , 1 )

MIDPOINT(0,1)

But now you have uncountable many choice functions!
One for each SET!

| N | = | GODEL NUMBERS |
| GODEL NUMBERS | = | FUNCTIONS |
| FUNCTIONS | = | CHOICE FUNCTIONS |
| CHOICE FUNCTIONS | = | ELEMENTS |
| ELEMENTS | = | SETS |
| SETS | > | N |

Once of these must be incorrect!
The only further resolution for Z.F.C. is
Uncountable Many Functions

| GODEL NUMBERS | < | FUNCTIONS |

Which means the WFF include Infinite Length Formula!

Such As:

IF SET1 has 1 - then MYSET skips 1 ./
or
IF SET1 skips 1 - then MYSET has 1

AND
IF SET2 has 2 - then MYSET skips 2 ./
or
IF SET2 skips 2 - then MYSET has 2

AND
IF SET3 has 3 - then MYSET skips 3
or
IF SET3 skips 3 - then MYSET has 3 .
...

CANTORS MISSING SET FORMULA
when expanded out to infinitely many terms.

You probably recognise the above as:

{ n | n ~e f(n) }

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

Herc
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