Date: Apr 23, 2013 4:01 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Matheology § 258
Matheology § 258

So what about Cantor?s much celebrated non-denumerable real? Where is

it? Did Cantor produce such a real number? No, he merely sketched out

the logic for a nonterminal procedure that would produce an infinitely

long digit string representing a real number that would not be in the

input stream of enumerated reals. Cantor?s procedure, and with it his

celebrated nondenumerable, infinitely long real number, will appear

with 100% certainty in the denumerable list of procedures. {{That's

the point: Every diagonal number can be distinguished at a finite

position from every other number. But if all strings are there to any

finite dephts, as is easily visualized in the Binary Tree, then there

is no chance for distinction at a finite position - and other

positions are not available.}}

There is no non-denumerable real, and every source of real numbers

is denumerable [...] Implications throughout mathematics that build

upon Cantor?s Diagonal Proof must now be carefully reconsidered.

So Who Won? Professor Leopold Kronecker was right. Irrationals are

not real {{ - at least they have no real strings of digits, and only

countably many of them can be defined in a language that can be

spoken, learned and understood}}. God made all the integers and Man

made all the rest {{and in addition something more - unfortunately.}}

[Brian L. Crissey: "Kronecker 1, Cantor 0: The End of a Hundred Years?

War"]

http://www.briancrissey.info/files/Kronecker1Cantor0.pdf

Regards, WM