Re: how

On 4/30/24 8:56 AM, WM wrote:

Le 27/04/2024 à 19:27, Richard Damon a écrit :

On 4/27/24 10:36 AM, WM wrote:

 

But since it isn't in the set, you can't use it as the value to "step back" to.

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The question was whether it is an upper bound. Bounds need not belong to a set.

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They do if you want to use them to step into the set, like you did.

 I use the upper bond only as uoper bound.

But then you can't talk about using it to "step back" from omega.
Yes, ALL Natural Numbers are less than omega.
That doesn't mean there is a largest Natural Number.
In fact, the fact that the smallest Upper Bound we can find is Omega, which is out of the set of Natural Numbers means that there is no "Highest" Natural number.

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Note, that value isn't "of the set that is below ω".

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Therefore this set ends before.

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Only if it HAS an "end"

 The end is smaller than ω.
 Regards, WM

But there isn't a specific number that is the end.
That is the problem with your logic.