What's the point of converging numbers anyway, from a purely number point of view.
Remember Zeno? He proved that you can't cross a room. In fact he proved you couldn't move at all. Understand Zeno's paradox first. Everybody knew he was wrong but no one knew how to prove it until the calculus. I may be wrong about this but I don't know of any proofs before that.
Why can't a series of numbers just continue forever? Why can't it just get infinitly smaller, who cares, they are just numbers.
Well they can. There are all kinds of series and some are very weird.
Note that there are series, and then the sum of a series.
.999... is a number, it's not a series. We did at various points in the explication say it was equivalent to the sum of the series .9+.09+.009... which it is. It was a way of explaining why this is true: .999... = 1.
If you take some math classes, which I think would be fun, you will find math uses very precise definitions except where it can't. Like a point and a line, even number have to be understood but from there on you can precisely difine what you mean. Part of your confusions in this thread was because you confused terms. Once you get the terms sorted out it will be clearer.
lfen