Re: The non-existence of "dark numbers"

Am Sat, 22 Mar 2025 10:19:13 +0100 schrieb WM:

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!).

That a superset contains elements the subset doesn't is trivial.
Whatever your intuition about "number of elements", it isn't cardinality.
How would you even determine equal sizes of infinite sets?

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.

That's bullshit. Bijections are "complete".

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.

Invisible = gone.

--
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.