Thanks Smo. I agree that we do have a well-defined definition of .999…, but most people are only accidentally using that definition. That is, kids who wonder what .999… means aren’t thinking “Gee, can someone compute the limit of the following sequence: …” but instead something like “What is the closest number I can get to 1 without (apparently) touching it?”

Intuitively, if you accept the idea of infinitesimals, you can say “There’s a possibility of getting infinitely close without touching. Standing on the line doesn’t mean you’re playing in the field.” and if you don’t, you’d say “There’s no way to represent an infinitely small gap, so you are either touching 1.0 or not, and .999… counts as touching. On the line is in the field.”.

Hi Rohit, thanks for the note!