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From: Ben Bacarisse <ben@bsb.me.uk>
Newsgroups: comp.theory
Subject: Re: Another proof: The Halting Problem Is Undecidable.
Date: Sun, 13 Oct 2024 22:01:02 +0100
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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.

-- 
Ben.