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NNTP-Posting-Date: Mon, 19 Aug 2024 00:42:29 +0000
Subject: Re: Replacement of Cardinality (selective memory)
Newsgroups: sci.math
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From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Sun, 18 Aug 2024 17:42:31 -0700
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On 08/18/2024 02:15 PM, Ross Finlayson wrote:
> On 08/18/2024 11:52 AM, Chris M. Thomasson wrote:
>> On 8/18/2024 1:16 AM, joes wrote:
>>> Am Sat, 17 Aug 2024 13:39:52 +0000 schrieb WM:
>>>> Le 16/08/2024 à 20:11, joes a écrit :
>>>>> Am Fri, 16 Aug 2024 17:00:26 +0000 schrieb WM:
>>>>>> Le 16/08/2024 à 18:50, joes a écrit :
>>>>>>> Am Fri, 16 Aug 2024 16:19:17 +0000 schrieb WM:
>>>>>>
>>>>>>> Taking steps only until the next unit fraction, you never reach 0.
>>>>>> Start from x = 0. The increase cannot be more than 1.
>>>>> No, you were counting down from 1.
>>>> There we see that counting down to 0 requires dark numbers.
>>> Counting down from infinity is not possible. Your "dark" numbers
>>> are a nonstandard extension.
>>>
>>
>> Yup. Counting down from infinity is moronic. No wonder why WM assumes
>> there is a place to start counting from, aka finite...
>
> Hey, it was Cantor's idea first, ....
>
>

Of course also Cantor had a theory with the domain principle,
where the Domainprinzip is that there's a universe of objects,
because basically he took everything he could find of an historical
study of infinity and wrote it in set theory a theory of one relation
and kept whatever sticked.

These days this is called "Cantor's Paradox", because the part
he kept, which is a very simplest sort of concept of the set of
all sets that don't contain themselves containing themself
that later Russell also appropriated and called "Russell's Paradox"
about the set of all sets that don't contain themselves, and
the very simplest sort of quantification, the part he kept
and the part where there's a universe of set-theoretical objects
don't agree.


It's funny that when the putative function of Cantor's
theorem is successor in a usual ordinal sense that the
only missing bit is empty set, then, for example, that
in theory's without empty set, it's not a thing, and in
another where ordinal's aren't the empty set, it's,
not a thing.

Empty set, universal set, ..., some theories don't have them.