Re: small but infinite sets

David R Tribble writes:
>> But while we can repeat the action any number of
>> times and still end up with an infinite set, we obviously can't repeat
>> the action an _infinite_ number of times, or else we'd remove all of
>> the elements from the set.
>

Dave Seaman wrote:
> Doesn't the Sieve of Eratosthenes remove an infinite number of terms
> infinitely many times, and still leave infinitely many numbers in the
> set?

Well, yes, but I was specifically referring to ***'s example, which if
I understand it correctly, removes "all elements not of the form X",
then proceeds to repeat that action and in the process removes the
smallest element, which is now not "of the form X", making some other
larger element the new smallest element. I got the impression that
his process would remove all the elements if repeated an infinite
number of times.

But obviously if a procedural step does not remove some elements that
were not removed in a previous step, then, sure, that procedure can be
repeated an infinite number of times and still leave an infinite set.

.

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