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From: Alan Mackenzie <acm@muc.de>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit fractions?
Date: Sat, 5 Oct 2024 13:57:30 -0000 (UTC)
Organization: muc.de e.V.
Message-ID: <vdrgka$sn2$3@news.muc.de>
References: <vb4rde$22fb4$2@solani.org>   <vdo8ke$586f$3@dont-email.me> <vdodmu$5sti$4@dont-email.me> <vdoeft$6biq$1@dont-email.me> <vdof0j$5suf$3@dont-email.me> <vdogjq$6l4c$1@dont-email.me> <vdpbuv$alvo$1@dont-email.me> <8c94a117d7ddaba3e7858116dc5bc7c66a46c405@i2pn2.org> <vdqttc$mnhd$1@dont-email.me> <vdr1g3$n3li$6@dont-email.me> <8ce3fac3a0c92d85c72fec966d424548baebe5af@i2pn2.org> <vdrd5q$sn2$2@news.muc.de> <55cbb075e2f793e3c52f55af73c82c61d2ce8d44@i2pn2.org>
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Richard Damon <richard@damon-family.org> wrote:
> On 10/5/24 8:58 AM, Alan Mackenzie wrote:
>> Richard Damon <richard@damon-family.org> wrote:

>> [ .... ]

>>> But actual infinity doesn't exist.

>> What does it mean for a mathematical concept not to exist?

> That it doesn't create a usable (non-contradictory) logical system.

Yes!  At least, sort of.  My understanding of "doesn't exist" is either
the concept is not (yet?) developed mathematically, or it leads to
contradictions.  WM's "dark numbers" certainly fall into the first
category, and possibly the second, too.

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

Does "actual infinity" create a logical system?  If so, what is unusable
or contradictory about that system?

[ .... ]

-- 
Alan Mackenzie (Nuremberg, Germany).