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From: Moebius <invalid@example.invalid>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Sat, 28 Dec 2024 20:42:51 +0100
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Am 28.12.2024 um 06:28 schrieb Moebius:
> Am 28.12.2024 um 06:23 schrieb Moebius:
>>
>>>> On 12/17/24 4:51 PM, WM wrote:
>>
>>>>> all FISONs contain/are all n.
>>
>> Mumbo-jumbo.
>>
>> Hint: For each and every n e IN there is a FISON such that n is in it.
>>
>> BUT there's no FISON such that each and every n e IN is in it.
> 
> Mückenheim: "all singletons contain/are all n".
> 
> Hint: For each and every n e IN there is a singleton such that n is in 
> it (namely {n}).
> 
> BUT there's no singleton such that each and every n e IN is in it.
> 
> <facepalm>

On the other hand, _the UNION of_ all FISONs contains all n e IN.

In the same way, _the UNION of_ all "IN-singletons" contains all n e IN.

Using symbols: U_(n e IN) {m e IN : m < n} = IN and U_(n e IN) {n} = IN.

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