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From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: The non-existence of "dark numbers"
Date: Sat, 22 Mar 2025 11:14:04 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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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.