| vlad321 said: So here it goes, I hope this is not a joke thread because I'm about to waste 3 minutes of my life writing this up. From here on out S is sigma 0.999999 can be represented as the infinite sum of S(9 * (1/10) ^n) where n = 1 to infinity.This is basically sayying that 0.99999... = 9/10 +9/100 +9/1000 +.... Meanwhile the sum of a geometric series is PROVEN to be equal to : a/(1-(1/r)) Where a is the first term, 0.9 in this case, and r is the rate of growth, 1/10 in this case. So where does that leave us? 0.9/(1-(1/10) = = 0.9/( 9/10) = = 0.9/0.9 = = 1
And that is the easiest and way to prove this. The whole 0.3333 = 1/3rd is crap and not a real proof by any stretch of the imagination. |
Of course that it is proof. You can't belittle it just because it doesn't have a pretty geometric equation to it. Sure, what you wrote down is true, but you can't do, is prove that 0.(3)= 1/3 isn't true. Why? You would do in the whole 0.(9) theory, and that you can't do, since you proved it.
Math is not about making things complicated, sheesh..
Huh. Who would've thought that beggining anew in my real life would coincide with starting anew on vgchartz?
Any day now, the dollar will be worth less than 2 zloty......any day now.....and my life savings will be in total jepordy ;(.
