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From: Moebius <invalid@example.invalid>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions?
Date: Sun, 15 Sep 2024 02:07:51 +0200
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Am 15.09.2024 um 01:54 schrieb Chris M. Thomasson:
> On 9/14/2024 10:30 AM, FromTheRafters wrote:
>> WM presented the following explanation :
>>> On 14.09.2024 01:05, FromTheRafters wrote:
>>>> WM explained :
>>>
>>>>> No, that is your big mistake. In the interval [0, 1] there is a 
>>>>> point next to 0 and a point next to 1, and infinitely many are 
>>>>> beteen them.
>>>>
>>>> Define 'next [to]' in this context.
>>>
>>> Two points are next to each other means that no point is between them.
>>
>> So which point is next to zero. Is it rational, or is it irrational? 
>> In either case it is greater than zero and there is again more room 
>> for an even closer number.

If r e IR, r > 0, then 0 < r/2 < r.

Hence there is no real number > 0 "next to 0".

> WM says .00001 is next to zero... Ahhh shit, what about .000001?