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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: collective and individual removal
Date: Mon, 28 Apr 2025 21:54:31 +0200
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On 28.04.2025 16:04, FromTheRafters wrote:
> WM explained on 4/28/2025 :
>> We can remove collectively all terms from the harmonic series. Nothing 
>> remains.
>>
>> If we restrict the removal to individually definable terms, then an 
>> infinity remains.
>>
>> Is this remainder caused by the impossibility to define infinitely 
>> many terms individually? No! It is sufficient to define one term, 
>> namely the last one definable.
> 
> But there is no last one definable

That is true. They are a potentially infinite sequence.

> since they all are.

That is wrong because you cannot remove all natural numbers by removing 
only definable numbers

Regards, WM