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From: Keith Thompson <Keith.S.Thompson+u@gmail.com>
Newsgroups: comp.theory
Subject: Re: Repeating decimals are irrational
Date: Tue, 26 Mar 2024 17:53:30 -0700
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wij <wyniijj5@gmail.com> writes:
> On Tue, 2024-03-26 at 17:28 -0700, Keith Thompson wrote:
[...]
>> So you're saying that 0.333... is not exactly equal to 1/3.
>> 
>> It seems odd that you agree that 0.999... is exactly equal to 1, but
>> 0.333... is not exactly equal to 1/3.
>> 
>
> I say the limit of 0.999... is 1, not 0.999... is 1. (this is also what you asked)
> Read the definition carefully from trustworthy website.

So you're distinguishing between "the limit of 0.999..." and "0.999...".

I see no difference between them.  To me, the "..." notation *means* the
limit.  Can you explain what difference you see?

When I write "0.999...", I mean the limit as the number of 9s increases
without bound.  That limit, I think we both agree, is equal to 1.  And
perhaps we also both agree that the limit of 0.333... as the number of
3s increases without bound is equal to 1/3.

Are you saying that:

- 0.999... is something other than the limit as the number of 9s
  increases without bound?
- 0.999... is a real number?
- 0.999... is less than 1?

If so, what is the real value of 1 - 0.999...?

[...]

-- 
Keith Thompson (The_Other_Keith) Keith.S.Thompson+u@gmail.com
Working, but not speaking, for Medtronic
void Void(void) { Void(); } /* The recursive call of the void */