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

WM formulated on Wednesday :

On 16.10.2024 13:54, Richard Damon wrote:

On 10/16/24 4:30 AM, WM wrote:

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There is a general rule not open to further discussion:
When doubling natural numbers we obtain even numbers which have not been doubled.
In potential infinity we obtain more even natural numbers than have been doubled.
In actual infinity we double ℕ and obtain neither ℕ or a subset of ℕ.
>

But that isn't actually a general rule,

>
It is a general rule that doubling creates larger numbers.

It is a general rule that doubling finite cardinal numbers creates larger finite cardinal numbers. In transfinite cardinalities Aleph_Zero times two is still Aleph_zero though.