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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, 29 Oct 2024 09:36:27 +0100
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On 29.10.2024 00:58, Richard Damon wrote:
> On 10/28/24 3:42 PM, WM wrote:

>> I mean that there are unit fractions.
>> None is below zero.
>> Mathematics proves that never more than one is at any point.
>>
> Which doesn't mean there must be a first, as they aproach an 
> accumulation point where the density becomes infinite.

Their density is bounded by uncountably many points between every pair 
of consecutive unit fractions:
∀n ∈ ℕ: 1/n - 1/(n+1) > 0.
The density is one point over uncountably many points, that is rather 
precisely 0.
> 
> Something which can't happen your world of finite logic, but does when 
> the logic can handle infinities.

Where does the density surpass 1/10? Can you find this point? If not it 
is another proof of dark numbers.

Regards, WM