Re: how

On 4/25/24 4:15 PM, WM wrote:

Le 25/04/2024 à 01:13, Richard Damon a écrit :

On 4/24/24 1:05 PM, WM wrote:

 

Is there an ordinal between ℕ and ω? If not, then the next number below ω is a natural.

>
Nope, because "next below" is not an operation defined for ω, just like it isn't for 0.

 Defined or not, there is something on the way from 1 to ω. Only natural numbers or empty steps.

But there is no "step" to ω from the value before it, only the hyper step from the full set of finite numbers.

>
The ONLY numbers below ω are the Natural Numbers, but "next" doesn't apply.

 If ω is existing, then something is next.

next above, yes, ω+1
next below, no, the problem is the set below it is unbounded, and thus doesn't have a "highest" value in it.

 Regards, WM