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From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions?
Date: Mon, 9 Sep 2024 11:51:33 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Mon, 09 Sep 2024 12:31:55 +0200 schrieb WM:
> On 08.09.2024 22:11, Richard Damon wrote:
>> On 9/8/24 3:52 PM, WM wrote:
>>> On 07.09.2024 16:51, Richard Damon wrote:
>>>> On 9/7/24 9:45 AM, WM wrote:
>>>
>>>>> Because ℵo unit fractions have ℵo gaps. We can use one of the gaps
>>>>> as x  > 0.
>>>> But you started with that x, so it was fixed to begin with.
>>> No, it is the size of one of the gaps between two adjacent unit
>>> fractions, ℵo of which are claimed to fit into (0, x).
>> So it is the size of *ONE* of the gaps, you need to choose which one,
>> as all the gaps are different sizes.
> And all gaps are occupied by the unit fractions. Hence every gap is too
> small.
In which sense are the gaps „occupied”?

>> Remember, just as there is no smallest unit fraction, there is no
>> smallest gap, so you can't specify choosing the smallest.
>> The fact that the choice is for ANY, it requires you to actually CHOOSE
>> one, and then we can find the Aleph_0 smaller.
> No. First you claim the unit fractions with their gaps. Then I choose
> one of them, irrelevant which one. Each one is smaller than all.
Each gap is smaller than all gaps?

-- 
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.