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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Date: Tue, 29 Oct 2024 15:16:50 -0700
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On 10/29/2024 4:55 AM, joes wrote:
> Am Tue, 29 Oct 2024 09:36:27 +0100 schrieb WM:
>> 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:
>> The density is one point over uncountably many points, that is rather
>> precisely 0.
> So not bounded at all.
> 
>>> 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?
> How do you define the density at a point?
> 

You need two points to get a difference that is non zero.