Re: Cantor's diagonal proof wrong?

From: Shmuel (Seymour J.) Metz (spamtrap_at_library.lspace.org.invalid)
Date: 11/22/04 

Date: Sun, 21 Nov 2004 20:50:50 -0500

In <f2c35871.0411180147.6252ca24@posting.google.com>, on 11/18/2004
   at 01:47 AM, imaginatorium@despammed.com (Brian Chandler) said:

>Well, since the OP clearly intended 8 to mean eight, and 7 to mean
>seven, then the sum is naturally defined using the standard carry.

The standard carry is only defined for decimal expansions of integers.
It is not defined for infinite sequences of integers. You can provide
a definition, but if you do it will break some expected properties of
the integers.

>Am I right, though, in saying that it is clear that these things at
>least form a ring?

Not unless you define + and * in such a way that the ring properties
hold. In fact, it will take some work to even make them form a group. 

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