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Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Re: Cantor Paradox
Replies: 17   Last Post: Mar 15, 2004 12:45 PM

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Danny Purvis

Posts: 176
Registered: 12/6/04
Re: Cantor Paradox
Posted: Mar 11, 2004 11:09 AM
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On 11 Mar 2004, Virgil wrote:

>Even more, Nathan¹s list, if it can exist at all, is already an
>infinite string and it must be given before the diagonal can be
>constructed.
>
>Which means that any "diagonal" requires an infinite string, the
>list, for its definition.


I'm having trouble seeing this point. Why would this same objection
not apply to the standard argument showing the reals are not
denumerable? It seems to me that Nathan can construct his diagonal
as far out as he wants to, one step at a time, just the way the
diagonal in the standard argument is constructed, only assuming the
availability of an algorithm for translating strings to real numbers.

Danny Purvis

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