Re: Zenkin's paper on Cantor (reply of Dr. Zenkin)

From: Shmuel (Seymour J.) Metz (spamtrap_at_library.lspace.org.invalid)
Date: 11/15/04 

Date: Mon, 15 Nov 2004 03:25:25 -0500

In <320e992a.0411140136.75b1a6fe@posting.google.com>, on 11/14/2004
   at 01:36 AM, examachine@gmail.com (Eray Ozkural exa) said:

>If you understand the terms, it can be mathematics.

The inability to formulate a definition usually indicates that you
don't understand the terms. Definitions in Mathematics are omitted
only when they are commonly agreed upon, and even then it is customary
to set forth the nomenclature used to avoid ambiguity. Using a
nonstandard term without a definition is a sign of sloppy thinking and
is a red flag.

>While the truth of Cantor's theorem follows from ZFC in a finite
>number of steps (this is easily seen!), I must admit that I cannot
>readily observe how Cantor's diagonal *proof* terminates in a finite
>number of steps.

A proof is not an automaton. A proof is not an algorithm. A proof is a
series of applications of rules of inference. It doesn't start and
stop, it just is. Every step lies there for your examination. 

-- 
Shmuel (Seymour J.) Metz, SysProg and JOAT  <http://patriot.net/~shmuel>
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