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

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

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Virgil

Posts: 4,486
Registered: 1/6/11
Re: The Diagonal Argument
Posted: Dec 28, 2012 12:35 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

In article
<c3b9462b-6826-46fd-bfe3-39c2d95ab507@pe9g2000pbc.googlegroups.com>,
Graham Cooper <grahamcooper7@gmail.com> wrote:

> one must consider the audience Virgil!
>
> SWAPPING DIGITS DOWN THE DIAGONAL
>
> 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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