
Matheology § 258
Posted:
Apr 23, 2013 4:01 AM


Matheology § 258
So what about Cantor?s much celebrated nondenumerable 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 nondenumerable 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

