Re: Replacement of Cardinality

Le 23/08/2024 à 20:42, Jim Burns a écrit :

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.

>
How so?

>
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.

In cawsews with distances.

 Split ℚ⁺ the positive rationals into {p²≤2}ꟴ, {2≤p²}ꟴ
No rational √2 exists.

But the last rational approximation exists. It is dark.

Even so,
each two rationals are separated by a distance > 0.

Of course. But the necklace analogon is easier to comprehend.
Regards, WM