[quote=@Webmaster]
<Snipped quote by whizzball1>

The very fact that it continues forever proves that it's not exact. .3333... != 1/3 in the same way that 
(1/3 * 3 == 3/3 == 1) != (.33333... * 3 == .99999999...). By definition, .99999... != 1, as it is infinitesimally less than one, but to the degree that it is [i]essentially [/i]1. But no matter what point at, and how many digits out you go, .999999... isn't 1.
[/quote]

I always saw something like 0.333333... as representing the whole forever, just like the infinity sign represents all of infinity. I would suppose that it's an axiom problem, since you can either see a repeating decimal with a ... as representing the exact, forever-going value, or as "it goes on forever".

If, and only if, 0.333333 represents the exact value of 1/3, then, and only then, does the proof hold true.