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

On 02.11.2024 14:54, FromTheRafters wrote:

WM was thinking very hard :

 

That means, there is always another element. Potential infinity.

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Sets don't change. Forget about amplifying 'not finite' with such as 'actual' and potential' -- infinite simply means not finite and 'actual/potential' is a distinction without a difference. A useless concept outside of math philosophy.

 You are wrong because you cannot comprehend the difference between elapsing time and points of an interval.

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the set of denominators have no largest element to 'start' with.

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If all unit fractions are existing, then a smallest unit fraction is existing. If NUF(x) has grown to ℵ₀ at x₀, then ℵ₀ unit fractions must be between 0 and x₀. Hence at least ℵ₀ points with ℵ₀ intervals of uncountably many points must be between 0 and x₀. That cannot happen at x₀ = 0.
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Is that too hard to understand?

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Apparently, for you.

 Chuckle.
 Regards, WM