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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)
Date: Tue, 08 Oct 2024 16:33:16 -0400
Organization: Peripheral Visions
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joes explained on 10/8/2024 :
> Am Tue, 08 Oct 2024 17:26:43 +0200 schrieb WM:
>> On 08.10.2024 15:24, joes wrote:
>>> Am Tue, 08 Oct 2024 12:51:03 +0200 schrieb WM:
>>>> On 07.10.2024 17:18, joes wrote:
>>>>> Am Mon, 07 Oct 2024 11:08:33 +0200 schrieb WM:
>>>>>> On 07.10.2024 10:05, joes wrote:
>>>>>>> Am Mon, 07 Oct 2024 09:41:23 +0200 schrieb WM:
>>>>>>>> On 06.10.2024 17:48, Alan Mackenzie wrote:
>>>>>>>> even an unbounded sequence does not get longer when shifted by one
>>>>>>>> step.
>>>>>>> Nor does it get shorter, it stays infinite.
>>>>>> It keeps all its elements but not more.
>>>>> „More” being a different kind of infinity, namely at least
>>>>> uncountable.
>>>> Nonsense.
>>> Only according to your broken concept of cardinality, by which N u {a}
>>> is „bigger” than N, and N\{1} u {a} can’t even be compared.
> Clearly they are the same „size”.
>
>>>>> All ω+k are equally infinite.
>>>> Nonsense.
> This is your useless replacement of cardinality.
>
>>>>>>> Of course stopping after a finite number, which potential infinity
>>>>>>> seems to mean, is not „complete” in that sense. Hilbert’s Hotel is
>>>>>>> actually infinite, it already holds infinite guests.
>>>>>> Name them by all the natural numbers. Then no further guest can
>>>>>> appear.
>>>>> It can, if I begin numbering with 2. The cardinality of N\{1} can’t
>>>>> be finite.
>>>> Cardinality is nonsense.
>>> Isn’t N\{1} finite? It has ω-1 elements.
>> But after the visble natural numbers the dark domain comes, and that is
>> what prevents to see the end (which is dark too).
> But ω-1 is a finite natural.

No, that is like saying zero minus one is a natural number.