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

Revision as of 17:49, 30 March 2006

Revision as of 18:17, 30 March 2006

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:: 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)]

:::No. You're saying "For a given proposed enumeration (''x''_''n'') of the reals, Cantor presents a number ''c'' which is not captured. So let's just throw ''c'' in and we have enumerated the reals." The objection to your argument is: once you have thrown in ''c'', Cantor will happily present a ''new'' number (different from ''c'') that is still not covered by your new proposed enumeration. He will always catch you. [[User:AxelBoldt|AxelBoldt]] 18:17, 30 March 2006 (UTC)

:"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)