Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)

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⋅k is a finite and 2⋅k+2 > 2⋅k is not a finite.

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

--
Alan Mackenzie (Nuremberg, Germany).