.999... = 1

It does. Here:
1/3 = .333...
2/3 = .666...
3/3 = .999...
3/3 = 1
.999... = 1

Or you could look at it this way:
x = .999...
10x = 9.999...
10x - x = 9.999... - .999...
10x - x = 9x
9.999... - .999... = 9
9x = 9
x = 1
x = .999...
x = 1
x = .999...
x = 1
holy shit
.999... = 1
Take that, people.