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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?
Date: Mon, 9 Sep 2024 12:27:47 +0200
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On 08.09.2024 22:11, Richard Damon wrote:
> On 9/8/24 3:48 PM, WM wrote:

>> Select any gap between one of the first ℵo unit fractions and its 
>> neighbour. Call its size x. Then ℵo unit fractions cannot fit into the 
>> interval (0, x), independent of the actual size.
>>
> But that is changing the value of x in the middle of the problem which 
> isn't allowed.

No.
> 
> Given that new x, we can choose a new set of Aleph_0 unit fractions 
> below that x.

ℵo unit fractions are claimed to be smaller than every x > 0. If that is 
true then I can choose as the x one of the ℵo intervals between two of them.

Regards, WM