Re: how

Am 24.04.2024 um 19:09 schrieb WM:

Le 24/04/2024 à 03:52, Richard Damon a écrit :

On 4/23/24 2:35 PM, WM wrote:

Le 23/04/2024 à 00:58, Richard Damon a écrit :
>

you can only get to ω via a "hyper" step, not a normal step, like from 1 to 2.

Better use the term /jump/ for it (instead of "hyper step").

How many normal steps covers a hyper step?

"How many steps covers a jump?"
Depends, if it a jump to a natural or to, say, ω.
For every n e IN: the jump from n to ω "covers"

aleph_0

steps.

There is no ordinal between the finite numbers and ω.

Das hat auch niemand behauptet.

But something requiring ℵo steps. Looks like ordinals.

Ja, die ordinals/natnums between the number n and ω (for each and every n in IN).
Hint: For all n e IN: card({m e IN : n < m < ω}) = aleph_0.