Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)

WM expressed precisely :

On 19.10.2024 13:15, FromTheRafters wrote:

WM was thinking very hard :

On 19.10.2024 12:56, Jim Burns wrote:

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What is immediately before ω

No number exists immediately before ω

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Immediately or not: The number before ω is finite.

 No number is before omega,

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In analysis we have to deal only with the infinitely small and the infinitely large as a limit-notion, as something becoming, emerging, produced, i.e., as we put it, with the potential infinite. [Hilbert].

Is this from a 1925 lecture?

All these becoming, emerging, produced numbers

What does that even mean?

are numbers before ω.

Omega *IS* the ordered set of natural numbers, which is not finite.

Are they produced from nothing or are they produced from hitherto dark numbers? If  from nothing, then these numbers are the numbers before ω.
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omega is the naturally ordered set of natural numbers.

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That is another meaning of the word but not relevant, in particular not if there is no set of natural numbers because new numbers  can be produced and added.

???

ω-1 can't be infinite and must be infinite.

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ω-1 is a natural number

 No it is not.

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ω-1 is a natural number if ℕ is a set, i.e., if no new numbers are produced from nothing.

Minus one, for these infinite ordinals, is not defined.