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Originally posted by sonhouseThis arose again because of one silly post, asking one (what should have been) simple question. For those who accept silly little rules (calculus shmalculus) bask in your correctness. For self-proclaimed retards, two things are not "equal" unless the values on each side of the sign are the same.
Why do you need some kind of proof? Isn't it more of a definition?
, the infinite expansion of 0.999999...... by definition and calculus
= 1, end of story?
Originally posted by AlpineXazaxNo rounding is necessary. 0.999... = 1 because there is no finite difference between 0.999... and 1. Go ahead, pick a finite difference you think will work and try it. It's easy to show that for any difference you pick, you can get closer to 1 just by adding more terms in the series 9/10 + 9/10^2 + 9/10^3 + ... Since 0.999... implies the sum of an infinite number of terms, you need never worry about being too far away from 1 to be different than 1.
0.999999999..... is equal to 0.999999999..... because it is not whole and it never will be unless you round it, thus changeing the number.
Originally posted by sonhouseyou obviously skiped a few pages and missed the other thread
Of course it does, its the same thing as 0.99999.....=1. Its the
infinite sum of the digits we are talking about here, not just the
5 digits shown, the convention is the 0.999..... dot dot dot dot is
referring to that infinite sum.