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

On 19.10.2024 18:04, Jim Burns wrote:

On 10/19/2024 4:16 AM, WM wrote:

What you call a "set of finite ordinals" is
not a set
but a potentially infinite collection.

 There is a general rule not open to further discussion:
Finite sets aren't potentially infinite collections.

Potentially infinite collections are finite sets open to change.

Proof:
If you double all your finite ordinals
you obtain only finite ordinals again,

 Yes.
 

although the covered interval is
twice as large as the original interval
covered by "all" your finite ordinals.

 No.
The least.upper.bound of finites is ω
The least.upper.bound of doubled finites is ω

Doubling halves the density and doubles the interval, creating numbers which had not been doubled. 2n > n does not fail for any natural number.
Regards, WM