/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

>>77
1. Fact: Wrong.
2. Fact: True, better then the last fact at least.
3. Wrong, wrong and wrong.
2. How the fuck did you go back to 2? Anyway, this point does not follow from 2 in any logical sense, it's true, but faulty reasoning.
3. No. 0.999...=1 without any sort of successor function
4.Just what the fuck.


You seem to have assumed the reals are countably infinite, to be able to inductively reach any of the from this silly "sucessor" function, which makes no sense anyway.
How can you increase the last digit of an infinite sequence?

What s(pi)?

To repeat, Maths is harder than you think.

And I call it maths because it's a series (multiple) of interwoven disciplines. And also cause I'm a eurofag.