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From: WM <wolfgang.mueckenheim@tha.de>
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Le 21/04/2024 à 18:07, Moebius a écrit :
> Am 20.04.2024 um 20:34 schrieb WM:
>> Le 20/04/2024 à 19:42, FromTheRafters a écrit :
> 
>>> What is a gap in the ordinals?
>>> 
>> It is a not existing ordinal between two ordinals.
> 
> Aha, dann gibt es also zwischen allen Ordinalzahlen "gaps".

More precisely: A gap on the ordinal axis is a not existing ordinal in 
distance 1 from an existing ordinal. Example: Between -oo and 0 there us a 
huge gap.

>> It is a not existing natural number next to ω, for instance.
> 
> Ja, solche natürlichen Zahlen gibt es in der Tat nicht.

Below ω there is a huge gap or there are dark ordinals.
> 
>  > the idea that ω follows upon all natural numbers with no gap in between.
> 
> Hint: There is no "gap in between" in the following sense:
> 
> ω is (provably) the smallest ordinal AFTER (large than) all finite 
> ordinals. 

If so, then at ω-n there are gaps.

Regards, WM