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.

 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.

 

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?

 Apparently, for you.

Chuckle.
Regards, WM