This little guy craves the light of knowledge and wants to know why 0.999... = 1. He wants rigour, but he does accept proofs starting with any sort of premise.
Enlighten him.
so, start with:
x = 0.999...
now multiply each side by 10
10x = 9.9999....
now we subtract x from the left side, and 0.999... from the right, which is fine because they are equal:
9x = 9
and from there it should be fairly obvious that x is also equal to 1, which means 0.999... is also equal to 1