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

On 10/07/2024 09:11 AM, Alan Mackenzie wrote:

FromTheRafters <FTR@nomail.afraid.org> wrote:

Alan Mackenzie wrote :

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[ .... ]
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The idea of one countable set being "bigger" than another countable set is
simply nonsense.

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Oops. Finite sets are countable too. :)

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Yes indeed!  Thanks for pointing out my mistake.  What I should have
written (WM please take note) is:
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The idea of one countably infinite set being "bigger" than another
countably infinite set is simply nonsense.
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Oh, no, there are plenty of "size" relations given other
aspects that merely cardinality that have anything else
to do with what a set models.
For example, there's OUTPACING which makes for that
a proper superset of a set, is larger, by the OUTPACING
relation, it's a fact of mathematics.
And exactly half of the integers are even.
It's called density and it's a property of
them including sets of them.
You're about as bad.