Re: Repeating decimals are irrational

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 */