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

On 25.10.2024 16:53, Jim Burns wrote:

On 10/25/2024 7:42 AM, WM wrote:

The whole interval (0, ω) is not finite,
let alone the doubled interval.

 ⟦0,ω⦆ is the set of finite ordinals.
That is the definition of finite ordinal.
That is the definition of ω,
the first ordinal after all finite ordinals.

Correct so far.

 γ before ω: γ is finite.
γ ∈ ⟦0,ω⦆ ⇒
∀β ∈ ⦅0,γ⟧: ∃α: α+1=β
 ω before ξ: ξ is not finite.
ω ∈ ⦅0,ξ⟧ ⇒
¬∀β ∈ ⦅0,ξ⟧: ∃α: α+1=β
 (Keep in mind that ¬∃α: α+1=ω )

That is wrong in complete infinity.

A better question is:
why do you (WM) support it?

I support it in order to show that your infinity is inconsistent.
Example: Almost all unit fractions cannot be discerned by definable real numbers. If they are existing, they are indiscernible, i.e. dark.
Regards, WM