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Math Forum » Discussions » Inactive » Historia-Matematica

Topic: [HM] A question as to Cantor's Diagonal Method.
Replies: 13   Last Post: Oct 25, 2005 6:01 AM

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Roger Cooke

Posts: 242
Registered: 12/3/04
Re: [HM] A question as to Cantor's Diagonal Method.
Posted: Aug 30, 2005 10:39 AM
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I think this topic has been discussed before. In his personal notebooks,
Luzin speculated that the Cantor diagonal proof shows only that the real
numbers are not effectively enumerable. But I have always had trouble
understanding what it could mean to say that " |X| =3D |N| " is true if
no
such enumeration "exists." But I think William Waterhouse's objection
misses the point: the set X *is* the real numbers, by assumption. Of
course taking Z in place of X produces a different result: so what? Or
am I missing something myself?

Roger Cooke

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