Talk:Cantor's first set theory article/Archive 1: Difference between revisions

Revision as of 22:45, 6 June 2005

Revision as of 08:19, 27 September 2005

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: After carefully reading the above post, I conclude that the author is making a mistake similar to those made by many people encountering diagonal-method proofs for the first time. The problem is that if the initial set chosen is {X1,X2,X3, ... C} (with C inserted between two Xi's -- this is not captured by the notation), then the limit value produced by Cantor's argument will not be C, but something else.

:: Even a good high school student would balk at the above objection --- are you saying that a monotone sequence could have a middle-term limit? [[e-mail] (27 Sep 2005)]

:"Cantor's first proof" is new to me, and I have to say it's delightful. I agree that mathematicians generally believe the diagonal argument to be Cantor's first. However, I'm not completely convinced that this isn't really a diagonal argument in disguise. I need to think about this a bit. [[User:Dmharvey|Dmharvey]] [[Image:User_dmharvey_sig.png]] [[User talk:Dmharvey|Talk]] 22:45, 6 Jun 2005 (UTC)