/prog/rammer here, need urgent help

hello /sci/, long time no see
There is currently a troll on /prog/, and would greatly appreciate your help.

Basically, the troll is trying to prove that 0.999~ =/= 1
Here are some of his arguments
http://stormtower.invisionplus.net/?mforum=stormtower&showtopic=97

I'm wondering if the maths genius' on this board can rip him apart? Thank you

>>72
1.
I'm not sure what exactly you're saying here. By 0.999... I mean zero point nine repeating, 0.(9), etc. I'm not sure how else to define it.

2.
If I'm not mistaken, the sum of an infinite geometric series is:
(first term) / [1 - (common ratio)], which is the formula I've used. So I'm not sure what you mean by,"applied a theorem on finite geometric series."

>>73
I'm not sure how this is relevant to anything...