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

On 11/28/24 7:20 AM, WM wrote:

On 27.11.2024 22:20, Richard Damon wrote:

On 11/27/24 3:09 PM, WM wrote:

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It is completed! Every number 10n starts wit a black hat.

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Right, and it gives that hat to n, so every number gets one.
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And, 10n will get back a hat from 100n, so it still have one at the end.
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It seems so, but that is impossible. Up to every 10n, the interval 1, 2, 3, ... 10n has a covering of 1/10 only. The limit of this sequence is 1/10 too. And since this is true for all natural numbers, where should additional hats come from?

No, it is possilbe,