Re: The non-existence of "dark numbers"

Am Sun, 23 Mar 2025 18:23:49 +0100 schrieb WM:

On 22.03.2025 20:33, Jim Burns wrote:

On 3/22/2025 5:19 AM, WM wrote:

 

It is infinite but nevertheless obeys the logic of lossless exchanges
do not suffer losses.

Infinite sets don't need to obey the logic of lossless exchanges do not
suffer losses.

Every set does because the claim concerns always only one finite term:
One single exchange.

Exactly. It does not concern the result, the limit.

The loss, if happened, had to happe at a finite index.

Uh no, then we wouldn't have an infinite sequence. It is your perennial
failure to conceptualise the infinite as something after every and all
finite indices.

The reason is that all pairs of the bijection proving same cardinality
have infinitely many dark successors which cannot be bijected.

A bijection which does not biject everything is not a bijection,

So it is! But it is impossible to prove everything in Cantor's
bijections. Almost all elements follow upon every defined pair.

...which are bijected just the same. Why should that change?

--
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.