Re: The non-existence of "dark numbers"

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

Of course.
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.
Regards, WM