/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

>>42
>>46
#1 isn't even a "proof", it's a question.  The proof would be to show that the answer to the question is "none".

#2 is ignorant bullshit.

#3 assumes that termwise multiplication of an infinite series by a constant is valid (which is true of course, but not justified or even mentioned).

There are a crapload of proofs given at http://en.wikipedia.org/wiki/.999#Proofs, one or two of which might even be valid.