Re: Another proof: The Halting Problem Is Undecidable.

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.