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NNTP-Posting-Date: Mon, 30 Dec 2024 02:04:35 +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, 29 Dec 2024 18:04:48 -0800
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On 08/18/2024 05:42 PM, Ross Finlayson wrote:
> 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.
>
>