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

On 12/20/24 3:18 PM, Chris M. Thomasson wrote:

On 12/20/2024 6:38 AM, WM wrote:

On 20.12.2024 12:55, Chris M. Thomasson wrote:

On 12/20/2024 2:13 AM, WM wrote:

On 20.12.2024 03:52, Richard Damon wrote:
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He builds an infinite sequence that pairs a natural number to every rational number .

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And I build an infinite sequence of intervals [1, n] that contains every natural number.

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Cantor Pairing works will any of them.

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Therefore no interval [1, n] and therefore no n is missing in my proof that the pairing
10n --> n, n ∈ ℕ
does not work. For every interval at least 9/10 are missing.

 Huh? Have you ever implemented Cantor Pairing and tried it out? It works with any unsigned integer. So, it works with all of them. Why do you seem to have trouble with it?

His problem is he isn't using the actual set of Natural Numbers, only a FISON of 1 to n, and thus a lot of the numbers don't have the needed 10xn available.