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From: Moebius <invalid@example.invalid>
Newsgroups: sci.math
Subject: Re: Does the number of nines increase?
Date: Tue, 16 Jul 2024 04:55:06 +0200
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Repost:

Am 16.07.2024 um 04:02 schrieb Chris M. Thomasson:
 > On 7/15/2024 6:57 PM, Moebius wrote:

 >> See? 😛

 > I see that you increased the granularity from natural numbers into 
the unit fractions...

Yeah, the real numbers comprise the naturals, the integers, the unit 
fractons, the rational numbers, ..., you know. 🙂

 > Wrt enumeration unit fractions I like to go from 1/1, to 1/2, to 1/3, 
ect...

You may like to do that, still:

0 < ... < 1/3 < 1/2 < 1/1.

Meaning: Concening the < relation as _defined on the reals_ (as well on 
the rationals) 1/3 is SMALLER than 1/2 and 1/2 is smaller than 1/1. In 
general: 1/(n+1) is smaller than 1/n.

 > Is that wrong?

Nope. You may define a SEQUENCE (of unit fractions):

(1/1, 1/2, 1/3, ...)

Here (referring to these sequence) 1/1 is "before", say, 1/2. 🙂

 > we have to think of a a smallest unit fraction, WM world, right?

Right. There simply is no such unit fraction because for each and every 
unit fraction u: 1/(1/u + 1) is a unit fraction that is smaller than u.