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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, 11 Dec 2024 16:51:18 +0100
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On 10.12.2024 19:18, Python wrote:
> Le 09/12/2024 à 22:50, WM a écrit :

>>>> The very core property of analysis is that equal sequences have 
>>>> equal limits if they have limits at all.
>>>
>>> E(1)∩E(2)∩...∩E(n) = E(n)
>>>
>>> Lim E(1)∩E(2)∩...∩E(n) = {}
>>> Lim E(n) = {}
>>>
>>> They are equal.
>>
>> Not in a set theory where every endsegment is infinite.
> 
> Nonsense.

In fact some readers claim that every endsegment is infinite. Finite 
endsegments cannot be seen. They are dark.
> 
> I once asked a whole classroom what they think of your claims, providing 
> your posts/site as well as Ben's paper : http://bsb.me.uk/dd-wealth.pdf. 

Ben Bacarisse's example : To keep things simple, let's number the notes 
1; 2; 3; : : : and we'll give McDuck only $2 a day. One has to be 
returned a day.

He accuses me to confuse lim card and card lim and to use the wrong 
limit. But I simply need the limit of the set only with no cardinality 
at all. Therefore his example is mistaken. I adhere to the additional 
condition though that a difference between two states can consist of one 
note only. That makes a sequence increasing beyond all bounds with limit 
empty set (where all elements are claimed to have gone) impossible.

Never a student of mine has doubted that.

Regards, WM