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From: Ben Bacarisse <ben@bsb.me.uk>
Newsgroups: comp.theory
Subject: Re: Another proof: The Halting Problem Is Undecidable.
Date: Mon, 14 Oct 2024 13:41:04 +0100
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wij <wyniijj5@gmail.com> writes:

> On Sun, 2024-10-13 at 22:01 +0100, Ben Bacarisse wrote:
>> wij <wyniijj5@gmail.com> writes:
>> 
>> > If 0.999..=1, you have to explain your arithmetic system.
>> 
>> Almost.  First you have to explain the notation.  That's easy (but
>> relatively advanced) as 0.999... denotes the limit of a sequence of
>> partial sums (sometimes called a series limit).  The arithmetic system
>> (the reals, where all such sums converge) comes after saying what the
>> ... denotes.
>> 
>> When *you* say that 0.999... =/= 1 you always avoid saying what the
>> notation (specifically the ...) means in formal terms.
>
> What I would say now is probably not different from
> https://sourceforge.net/projects/cscall/files/MisFiles/RealNumber2-en.txt/download
>
> "..." conventionally means "so on,..,etc.", likely infinitely. I use
> it like that.

So it might even be finite and it has some element of likelihood about
it?  I'll stick with the actual conventional meaning, thanks.

-- 
Ben.