Re: Incompleteness of Cantor's enumeration of the rational numbers

On 26.11.2024 18:50, Richard Damon wrote:

On 11/26/24 11:59 AM, WM wrote:

On 26.11.2024 16:06, Richard Damon wrote:

On 11/26/24 6:24 AM, WM wrote:

On 26.11.2024 12:15, FromTheRafters wrote:

WM pretended :

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It is impossible to change |ℕ| by 1 or more.

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Right, sets don't change. The set {2,3,4,...} does not equal the set of natural numbers, but |{2,3,4,...}| does equal |N|.
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Then your |N| is an imprecise measure. My |N| is precise.
|{2,3,4,...}| = |N| - 1 =/= |N| .

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Then your measure is incorrect, as by the DEFINITION of measures of infinite sets, all countably infinite sets have the same "measure".

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That is one special definition of a very imprecise measure. We can do better.

 But maybe you can't and get something consistant.

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Of course. |{1, 2, 3, 4, ...}| = |ℕ| and |{2, 3, 4, ...}| = |ℕ| - 1 is consistent.