/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

  Maybe all you programmers and math people can clarify something for me. I've been considering majoring in CS, however, the question of it's academic content has bugged me. How much theoretical computer science does the average cs degree entail as opposed to coding?
 
  From a philosophical viewpoint, stuff like questions regarding computability, Church Turing thesis, halting problem, etc. are very cool but how often does this stuff surface as opposed to time spent learning the idiosyncrasies of some language?