Re: how

On 4/26/24 1:02 PM, WM wrote:

Le 26/04/2024 à 16:49, Richard Damon a écrit :

On 4/26/24 10:41 AM, WM wrote:

 

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The set is bounded by ω.

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But ω isn't in the set, so it can't be the upper bound of the set that is below ω

 Learn the meaning of upper bound. ω*2 is an upper bound too.

But since it isn't in the set, you can't use it as the value to "step back" to.
Note, that value isn't "of the set that is below ω".

 Fact is that below ω there are natnumbers and above there are none. Hence they cease below the bound ω.

Yes, but it can't be the "Upper Bound" used to step back to from ω.
There is not "Upper Bound" for the Natural Numbers *IN* the Natural Numbers to be the "last" value to step back to.
Thus, your logic about ω-1 breaks. The value does not exist, as there can not be a "transfinite" value below ω, by its definition, and ω-1 can't be a Natural Number, as then it would be the "last" Natural Number, but that set doesn't have a "last" member, as its "Upper Bound" is outside the set, as it is a "Unbounded" set.

 Regards, WM