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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? (infinitary)
Date: Sun, 20 Oct 2024 09:21:46 -0000 (UTC)
Organization: muc.de e.V.
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WM <wolfgang.mueckenheim@tha.de> wrote:
> On 20.10.2024 00:54, Jim Burns wrote:
>> On 10/19/2024 2:19 PM, WM wrote:

>> A doubled finite is finite.

> If all finites are doubled, then not all results can be in that set.
> Either more finites appear, or the results are infinite.

That's your intuition getting the better of you again.  When "all
finites" (by which I assume you mean natural numbers) are doubled, all
the doubled numbers are finite, too.  We're talking about a mapping
between infinite sets, not a process.  Nothing "appears".

If you think some of the doubled numbers are infinite, please give an
example of a natural number which when doubled becomes infinite.

>> No k exists such that
>> 2=E2=8B=85k is a finite and 2=E2=8B=85k+2 > 2=E2=8B=85k is not a finit=
e.

> All doubled numbers result in larger numbers. That cannot be avoided.

Of course, for n > 0, 2n > n.  That need not be avoided.

> Regards, WM

--=20
Alan Mackenzie (Nuremberg, Germany).