/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 can't believe anyone who has taken a math class higher than basic algebra still believe 0.999.... is not equal to 1. There are numerous proofs that they are equal. I'll give you a few basic ones to start.

1. Between any two non-equal numbers in the set of rationals, there lies an infinite quantity of numbers. What number lies between 1 and 0.999....?

2. Take 1 - 0.999..... and you'll get that it equals 0.000.....1, which exactly equals 0. So the difference between 1 and 0.999... is exactly equal to 0.

3. 1/3 = 0.333....
   multiply both sides by three and you get
   3/3 = 0.999....
   1 = 0.999....

The whole thing seems obvious, even using 8th-grade level proofs....