/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

The only proof that is correct is the 1st one.

All use assumptions, but only the first one is an assumption that's basically definition (Depending on your definition).


2. Would require some sort of limit statement and use the fact that the reals are complete.

3. Requires you to justify algebraically manipulating infinite decimal expansions.

Whereas 1 merely relies on the completeness of the reals, which, as well as an ordering, defines them, so that's pretty much fine.


tl;dr? 1 is best, 2 is next, 3 is shit. State your assumptions before proofs.