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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Tue, 3 Dec 2024 12:46:26 +0100
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On 02.12.2024 20:06, joes wrote:
> Am Mon, 02 Dec 2024 17:51:22 +0100 schrieb WM:
>> On 02.12.2024 16:46, FromTheRafters wrote:
>>> WM wrote :
>>
>>>> E(1), E(2), E(3), ...
>>>> and E(1), E(1)∩E(2), E(1)∩E(2)∩E(3), ...
>>>> are identical for every n and in the limit because E(1)∩E(2)∩...∩E(n)
>>>> = E(n).
>>> Non sequitur. That which is true for finite sequences is not
>>> necessarily true for infinite sequences.
>> As easily can be obtaied from the above it is necessarily true that up
>> to every term and therefore also in the limit the sequences of
>> endsegments and of intersections are identical. Every contrary opinion
>> is matheology, outside of mathematics.
> What is the limit?

If infinity is actual, then the FISONs {1, 2, 3, ..., n} have a limit, 
then the limit of the sequence of FISONs is ℕ. Then the limit of the 
complementary endsegments is the empty set.

Regards, WM