FOM: Proper Names and the Diagonal Proof
silver_1 at mindspring.com
Wed Jun 26 12:08:27 EDT 2002
> Dean Buckner (6/24) wrote
>Cantor's proof has it otherwise. It says that we cannot "match" a set of
>ordinary names (numerals) to a set of names formed by infinite decimal
>expansion. Each row is "complete": it is a proper name formed out of an
>"infinite" collection of digits.
Don't think of a "collection" at all; think of infinitely long
sequences. To make it simpler, suppose the (infinitely long) sequences
consist of just 0's and 1's. For example, one of the sequences would start
out as: 0,1,0,0,0,1,1,...? (The '?' means that I don't know what comes
next.) Anyway, Cantor's proof goes through pretty much the same way....
(Notice that each sequence is open-ended to the right and therefore not
"complete," and there aren't any names, proper or improper.)
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