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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: Tue, 5 Nov 2024 17:49:26 +0100
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On 04.11.2024 22:46, Jim Burns wrote:
 > On 11/2/2024 5:28 PM, WM wrote:

 >> At least ℵ₀ points
 >> with ℵ₀ intervals of uncountably many points
 >> must be between 0 and x₀.
 >> This criterion is not satisfied by every point x > 0,
 >
 > No.
 > x₀ ≥ ⅟⌈n+⅟x₀⌉ > ⅟⌈n+1+⅟x₀⌉ > 0

That requires that x₀ is definable. But it is dark.

 >> but it is satisfied by
 >> every definable or visible point x > 0.
 >
 > every point.between.splits > 0 of
 > differences of ratios of countable.to numbers.

Of definable splits.

Regards, WM