Re: The non-existence of "dark numbers"

On 22.03.2025 06:11, Jim Burns wrote:

On 3/21/2025 2:15 PM, WM wrote:

On 21.03.2025 18:39, Jim Burns wrote:

On 3/21/2025 3:50 AM, WM wrote:

On 20.03.2025 23:25, Jim Burns wrote:

 

For sets not.having a WM.size,
Bob vanishing isn't a size.change.

>
Only if reducing isn't reducing.

>
What you (WM) think is reducing
isn't reducing.

>
You confuse
the clear fact that
in the reality of
sets vanishing means reducing
with
the foolish claim that
cardinality was a meaningful notion.

 The set of all sizes.which.WM.considers.sizes
does not have a size.which.WM.considers.a.size.

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

Learn that
even Cantor has accepted that
the positive numbers have more reality than
the even positive numbers.

 Without context, I can't be sure, but
I suspect that
Cantor's "more reality" and
Zermelo's "simplest" serve
the same purpose as my "emptier" and "fuller",
which is to rank infinite sets by
something _other than_ by size.

Cantor recognized that proper subsets have less substance than their sets. That is all and that is simple. Every child could understand it unless it had been stultified by matheologians with the result that all countable sets have the same cardinality (which is correct) and that this cardinality is a proof of same number of elements (which is wrong - wrong - wrong!).

He said that is not in conflict with
the identical cardinality of both sets.

 Thank you.
Two sets of the same cardinality,
one a proper subset of the other,
can be swapped set.wise, one for the other,
and preserve size.

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

Either swapping all at once,
or swapping in infinitely.many singleton.swaps,
size is preserved,
but reality;simplicity;fullness isn't preserved,
and Bob can disappear without leaving.

No. He can disappear from the visible part but not from the matrix.
Regards, WM