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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: collective and individual removal
Date: Mon, 28 Apr 2025 19:30:47 -0400
Organization: Peripheral Visions
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WM formulated the question :
> 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

Sure you can.