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:::No. You're saying "For a given proposed enumeration (''x''<sub>''n''</sub>) 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)
:::: This is the same commonest mistake in Cantor's diagonal argument --- once you have thrown in ''c'' and claim a complete list of the real numbers then you're done; a re-application of Cantor's diagonal argument does present a number (different from ''c'') but that new anti-diagonal number was included in the list when ''c'' was the anti-diagonal number. You merely made a new enumeration or re-arranged the row-listed real numbers to get a different anti-diagonal number! → I hope you teach my counter-counterargument to your counterargument in your math classes ... Best regards ... [BenCawaling@Yahoo.com (16 Oct 2006)]
:"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)
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