Talk:Cantor's diagonal argument/Arguments: Difference between revisions

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:::Now the conclusion of the theorem most definitely does NOT say there are no completed infinities. Quite the opposite! It relies on their existence from the outset. But only the explicit assumption is discarded by Cantor. <small>—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/66.67.96.142|66.67.96.142]] ([[User talk:66.67.96.142|talk]]) 05:30, 2 June 2008 (UTC)</small><!-- Template:UnsignedIP --> <!--Autosigned by SineBot-->

::::No, you are wrong. You will not find a single professional mathematician to agree with you on this. You ''will'' find ones who deny completed infinities, but that has nothing to do with it; your arguments are simple logical errors, plain and simple, and you cannot hijack the respectability of those mathematicians who deny the completed infinite to support these claims that have zero respectability. This is not the forum for discussing this and I should not have indulged you this long. When I get a chance I will move these non-editorial discussions to an "arguments" subpage. --[[User:Trovatore|Trovatore]] ([[User talk:Trovatore|talk]]) 07:30, 2 June 2008 (UTC)

::::It's clear from what you say that you have no idea what is meant by a 'completed infinite set'. Acceptance of CI is absolutely essential for Cantor's argument to work for the reasons stated above. You will find no respectable mathematician who accepts Cantor who does not also accept CI. Your last statement only exposes your shallow understanding of the subject. It's too bad, because if you knew what you were talking about, this article could be of value to readers.

Trovatore seems to be saying that the set of all infinite sequences of 0's and 1's is not a so-called "completed infinity". I'm not sure he really meant that. But I agree that some good mathematicians reject Cantorian Heaven with its well-ordered continuum, and that none will think the arguments given against it in this section are valid. If I were a good mathematician, I would be one of these people myself.