FOM: Proper Names and the Diagonal Proof

charles silver silver_1 at
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.)

Charlie Silver

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