/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

I don't know why I keep seeing the 1/3=.3333... proof, it assumes something that the opposing side believes to be false.

My own take on the topic is that the value of .9999... is something infinitely close to the number 1. The only thing that can be infinitely close to 1 is 1 itself. Thus, .9999... is just another way of saying 1.

Sage because I know nothing about math, and am just passing by.