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From: Moebius <invalid@example.invalid>
Newsgroups: sci.math
Subject: Re: Does the number of nines increase?
Date: Thu, 11 Jul 2024 00:07:26 +0200
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Am 10.07.2024 um 23:56 schrieb Chris M. Thomasson:
> On 7/9/2024 2:49 PM, Moebius wrote:

>> I guess you might have a _sequence_ of rational numbers in mind, say,
>>
>> (1, 1.4, 1.41, 1.414, ...).
>>
>> So we might say that this SEQUENCE represents the real number sqrt(2) 
>> - in a certain sense. :-P
>>
>> Actually, its limit is sqrt(2).
>>
> Well, basically, I was thinking that for any element of:
> 
> (1, 1.4, 1.41, 1.414, ...)
> 
> there is a rational that can represent it. 

lol. (Sorry!)

Which one, if I may ask? :-P

> So, it kind of makes my brain want to bleed from time to time, shit happens! Uggg. 

lol. (Sorry again!)

Imho you are "on a good way"!

Just take your time, and don't do the Mückenheim! :-)

> Taken to infinity, there are rationals that can represent [...] sqrt 2:
> 
> (1, 1.4, 1.41, 1.414, ...)

Yeah, but when speaking of a mathematical objekts (in this connection) 
we (usually) refer to the SEQUENCE (1, 1.4, 1.41, 1.414, ...)

Set theory allows to refer to such objekts (sets).

> However, there is no single rational that equals sqrt 2. 

Exactly! :-)

A thing even the ancient greeks new! :-P

> Humm... Fair enough?

Absolutely!