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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?
Date: Thu, 12 Sep 2024 11:24:18 -0700
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On 9/12/2024 4:18 AM, WM wrote:
> Le 12/09/2024 à 03:00, Richard Damon a écrit :
> 
>> So, you can't "index" an unbounded set of unit fractions from 0, as 
>> there isn't a "first" unit fraction from that end.
>>
>> We can "address" those unit fractions with the value, but we can not 
>> "index" them from 0, only from 1/1.
> 
> If you can index all unit fractions, then you can index them from every 
> side.

No. Thinking of using natural numbers to index them.

1 = 1/1
2 = 1/2
3 = 1/3
....

Since there is no _largest_ natural number, you cannot find the other 
end... See?


> Fact is that NUF(x) increases from 0, but at no point it can inc4rease 
> by more than 1 because of
> ∀n ∈ ℕ: 1/n - 1/(n+1) > 0
> Regards, WM
> 
>