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

Am Thu, 31 Oct 2024 18:28:15 +0100 schrieb WM:

On 31.10.2024 12:36, Richard Damon wrote:

On 10/30/24 7:53 AM, WM wrote:

 

NUF(0) = 0, NUF(1) = ℵo. Therefore NUF must grow but cannot grow by
more than 1 at any point x of the real axis.

Because it grows BETWEEN points on the real axis from 0 to ℵo.

I investigate its behaviour at single points.

At single points a function has a single value, not a jump. In the
case of NUF, that value is infinite everywhere except at 0.

Your problem is there isn't a "first" x > 0 above 0 to see it increase

We do not see dark numbers but I can prove their existence

Like all your non-questions, this is not about UFs but rather the
continuity of the reals.

 so it can just jump to ℵo.

But it cannot do so at a single point.

See above.

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Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.