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Topic: The Diagonal Argument
Replies: 28   Last Post: Dec 29, 2012 12:11 AM

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Registered: 1/6/11
Re: The Diagonal Argument
Posted: Dec 28, 2012 12:35 AM
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In article
Graham Cooper <> wrote:

> one must consider the audience Virgil!
> seems to be the only mathematics he can grasp!

Actually, Cantor's original argument does not even use digits.

Cantor considers the set, S, of functions from the set of naturals |N as
domain, to the two-letter set of letters {m,w}, and shows that there
cannot be any surjective mapping f: |N -> S by constructing a member g
of S not in Image(f)

Since f: |N -> S, each f(n) is a function from |N to {m,w}
So that when g(n) is a member of {m,w}\f(n)(n) for each n, then g is
not a member of S.

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