Re: how

On 4/20/24 12:39 PM, WM wrote:

Le 20/04/2024 à 01:32, Richard Damon a écrit :

On 4/19/24 11:37 AM, WM wrote:

 

Your logic can't double all natural numbers such that none below ω is missing. You create always new natural numbers. They have  not been doubled.

>
Nope. The whole countable infinity was always there

 Doubling doubles. The interval (0, ω) is doubled to (0, ω2).
 Regards, WM
 

Nope.
First, if we are talking the set of NATURAL Numbers, we don't normally talk about "intervals" like this, as (0, ω) would be the set {1, 2, 3, ...} and when doubled would be the set {2, 4, 6, ...} which isn't really an "inteval" any more as it skips values.
Intervals are more naturally used in continuous systems (like Rationals), and those are not normally talked about as "Ordianals", (as positions in sequences tends to be seen as discreet) and thus we don't get to ω which is defined as an ordinal. You are mixing domains and making category errors.