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.
I will be posting another another proof, one using the assumption that 0.999... is the sum of the series 9/10+9/100+9/1000+... (and that 1 is the sum of the series 1+0+0+0+...), unless somebody else comes here and feeds it to the little guy first.