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

On 10/14/24 9:40 AM, WM wrote:

On 14.10.2024 14:15, joes wrote:
 

No, we are taking the complete, actually infinite set which reaches
to "before" w.

 and fills the space between 0 and ω evenly. Same happens with the doubled set between 0 and ω2.
 Regards, WM
 

Nope, because omega wasn't in the first set, so since every element in the doubled set is also in the undoubled set, the ordinal "after" the set is still that original omega.
The problem is you seem to imagine the actual infinity as if it was finite and had a end, which it doesn't have.
If you can't imagine an actually created infinte set of numbers without an end, you can't imagine an actually created infinite set, since that is one of its properties.