Re: how

On 4/23/2024 6:50 PM, Richard Damon wrote:

On 4/23/24 2:06 PM, WM wrote:

Le 22/04/2024 à 20:02, FromTheRafters a écrit :

WM has brought this to us :

Le 21/04/2024 à 00:44, FromTheRafters a écrit :

WM wrote :

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What is a gap in the ordinals?

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It is a not existing ordinal between two ordinals. It is a not existing natural number next to ω, for instance.

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Sets do not have not existing elements.

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What is ω - 1?

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An absurdity.

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Not more nor less than ω.
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Regards, WM

 But if ω - 1 existed, it would be before ω, and thus less than it.

ω - 1 is undefined, however its always less than ω, kidding around here. Just like all natural numbers are less than ω. So, say ω - 1 = 0... rofl... Wow! lol. Fair enough for a jest, or interesting at all? Funny?

 That is the definition of ordinal numbers.
 But since it is NOT a "finite" number, as "ω - 1" + 1 would be ω and not a finite number, but all finite numbers + 1 give the next finite number, and ω is DEFINED as the first transfinite ordinal, it can not exist.