Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary, effectively)

Am 29.12.2024 um 03:13 schrieb Moebius:

Am 29.12.2024 um 03:07 schrieb Chris M. Thomasson:

On 12/28/2024 5:58 PM, Moebius wrote:

Am 29.12.2024 um 01:48 schrieb Chris M. Thomasson:
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Say, 1875520200019832...
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Each digit is random. This [represents] a number and it's within the infinite set of unsigned integers.

>
Nope. Such a "number" is not an integer.

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It's an unsigned integer at every step?

 Sure.
 For each and every n e IN the string
        d_n d_(n-1) ... d_0
 where d_i e {"0", "1", ..., "9"} for all i e {0, ..., n} represents an unsigned integer.

Actually,
       d_n d_(n-1) ... d_0
represents (denotes) the unsigned integer
       SUM_(k=0..n) [d_k] * 10^k ,
where ["0"] = 0, ["1"] = 1, ..., ["9"] = 9.
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