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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Date: Sat, 2 Nov 2024 18:36:28 +0100
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On 02.11.2024 13:30, joes wrote:
> Am Fri, 01 Nov 2024 11:07:27 +0100 schrieb WM:
>> On 31.10.2024 21:46, joes wrote:

>>> In the case of NUF, that value is infinite everywhere except at 0.

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.

Regards, WM