[johnhattan]

I remember a conversation I had with my daughter in the car when she was starting out with algebra...

Me: Is 9.999... the same as 10, or is it just really close to 10?

Kid: Really close. It never gets all the way there.

Me: Well then how close? What do you get when you subtract 9.999... from 10?

Kid: (pause) An infinite number of zeroes. . .and then a one. . .wait, you can't do that.

Me: Right. You just have an infinite number of zeroes. Which is zero.

Kid: (pause) Oh, that's mind-blowing.

[tomtomtom1]

> An infinite number of zeroes. . .and then a one. . .wait, you can't do that.

why not? why can't an infinitely small number exist?

[Sharlin]

It can, and infinitesimals are a part of so-called nonstandard analysis, but you cannot write an infinitesimal using decimal notation. "0.999…1" is simply meaningless, a contradiction. If you have a "…" it means there's no place where you could put a "last" digit. If "0.999…1" doesn't feel impossible enough, then what would "0.999…9" mean?

[hinkley]

People in this thread seem to think that “9 repeating” is not an infinity of nines but is instead “write or think of nines until you get bored and then write something else”

[dsabanin]

Because if it has 1 at the end, then this will mark it’s end, thus making it finitely small.