Re: Replacement of Cardinality

On 8/23/2024 10:32 AM, WM wrote:

Le 22/08/2024 à 19:24, joes a écrit :

Am Thu, 22 Aug 2024 11:07:42 +0000 schrieb WM:

Le 21/08/2024 à 20:14, joes a écrit :

The unit fractions get denser toward 0.
They are all positive.

>
They all have gaps.
This implies a last one if all are existing.

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How so?

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Every point is either in the empty domain
or in the populated domain.

One point is the last one in the populated domain.

Only in some cases.
Split ℚ⁺ the positive rationals into {p²≤2}ꟴ, {2≤p²}ꟴ
No rational √2 exists.
No last point in {p²≤2}ꟴ exists.
No first point in {2≤p²}ꟴ exists.
Even so,
each two rationals are separated by a distance > 0.