Re: The non-existence of "dark numbers"

On 24.03.2025 01:48, joes wrote:

Am Sun, 23 Mar 2025 20:36:12 +0100 schrieb WM:

Since it is completely irrelevant, we need not discuss this. Relevant is
only that mathematics breaks down and dissolves into matheology, when
exchanges defined to be lossless suffer losses.

This is very relevant in a discussion about infinity. And the "exchange"
which turns the initial state into the one after inf. many other
exchanges has no reason to be "lossless".

There is no state after infinitely many. Countable sets have the property that every element can be indexed by a finite index.

 

Swapping same.sized sets,
even same.sized proper.subsets and supersets,
is not a loss.

Swapping at finite indices means that finite logic rules, even in case
of a sequence of swaps with no last swap.

Yes, but the limit (after inf. many) has no finite index,

There is no limit. The claim states that every element gets a finite index.
Regards, WM
  and is thus

not subject to finite logic.