Re: how

On 4/20/24 2:31 PM, WM wrote:

Le 20/04/2024 à 19:05, Richard Damon a écrit :

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

 

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

 

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.

 The interval (0, ω2) is covered by {2, 4, 6, ...}.
 Regards, WM
  

But that interval would be actually { 1, 2, 3, 4, 5, 6, ..., ω, ω+1, ω+2, ...}
so, the interval notation is just incorrect as it includes members that aren't in the actual resutls.
So yes, the results are IN the interval, but are NOT THE interval.