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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions?
Date: Tue, 10 Sep 2024 08:03:50 -0400
Organization: i2pn2 (i2pn.org)
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On 9/9/24 11:19 AM, WM wrote:
> On 09.09.2024 13:51, joes wrote:
>> Am Mon, 09 Sep 2024 12:31:55 +0200 schrieb WM:
> 
>>> Al gaps are occupied by the unit fractions. Hence every gap is too
>>> small.
>> In which sense are the gaps „occupied”?
> 
> ℵo unit fractions cover a distance d which is the sum of the gaps 
> between them.
>>
>>> 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?
> 
> The sum of all gaps is larger than one of them.
> 
> Regards, WM
> 
> 

But there is an infinte set of gaps that will fit into any of them.

You keep getting your criteria order messed up.

Of course you can't fit ALL the Aleph_0 gaps into a smaller gap, but you 
CAN fit a subset of size Aleph_0 into there by removing the biggest ones 
until the total is small enough, and you will only need to remove a 
finite number of them, so you still have Aleph_0 left.

The fact that arithmetic blows you mind is why you have problems, you 
just don't understand the rules of arithmatic on infinite unbounded 
values, because you are stuck with the rule of just finite mathematics.