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

On 12/15/24 2:31 PM, WM wrote:

On 15.12.2024 13:52, Richard Damon wrote:

On 12/13/24 12:00 PM, WM wrote:

On 13.12.2024 13:11, Richard Damon wrote:
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Note, the pairing is not between some elements of N that are also in D, with other elements in N, but the elements of D and the elements on N.

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Yes all elements of D, as black hats attached to the elements 10n of ℕ, have to get attached to all elements of ℕ. There the simple shift from 10n to n (division by 10) is applied.  >

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No, the black hats are attached to the element of D, not N.

 The black hats _are_ the element of D.

No, the elements of D are the numbers that are 0 mod 10.

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But we aren't dealing with intervals of [1, n] but of the full set.

 All intervals together are the full set.

No, the full set is the full set.
Your "limit" argument is wrong, as is what lets us show that 0 == 1, proving that your logic has blown itself up.

 Regards, WM