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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: Wed, 18 Dec 2024 20:14:39 +0100
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On 18.12.2024 19:22, Jim Burns wrote:
> On 12/18/2024 7:40 AM, WM wrote:


>>> The infinite end.segments of finite.cardinals
>>> do not include any finite end.segments and
>>> they have an empty intersection.
>>
>> Explicitly wrong.
>> As long as only infinite endsegments are concerned their intersection 
>> is infinite.
>>
>> There are no limits involved.
> 
> Then it would be great if you (WM)
> stopped calling things 'limit sets'

The sets described here are not limit sets.
f(k) = ∩{E(1), E(2), ..., E(k)} with E(1) = ℕ
∀k ∈ ℕ : ∩{E(1), E(2), ..., E(k+1)} = ∩{E(1), E(2), ..., E(k)} \ {k},
∩{E(1), E(2), ...} is empty.
Other sets are not in the argument.

Regards, WM