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From: Moebius <invalid@example.invalid>
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Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions?
Date: Sat, 5 Oct 2024 16:58:10 +0200
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Am 05.10.2024 um 15:57 schrieb Alan Mackenzie:

> I first came across the terms "potential infinity" and "actual infinity"
> on this newsgroup, not in my degree course a few decades ago.  I'm not
> convinced there is any mathematically valid distinction between them.

Actually, there is.

But in classical mathematics "infinity" means "actual infinity", and 
"potential infinity" is of no significance her.

"Cantor's work was well received by some of the prominent
mathematicians of his day, such as Richard Dedekind. But his
willingness to regard infinite sets as objects to be treated in
much the same way as finite sets was bitterly attacked by others,
particularly Kronecker. There was no objection to a 'potential
infinity' in the form of an unending process, but an 'actual
infinity' in the form of a completed infinite set was harder to
accept."

(Herb Enderton, Elements of Set Theory)

> If there were, I would have heard of it back then.

Right.

> Does "actual infinity" create a logical system?

-> classical mathematics = ZFC (or something like that) + classical logic.