There is a problem with infinite decimal numbers : 0,9999... * 10 = 9,9999..., but it is harder to prove than we can think.
But still, 0,999... = 1 and there is another way to proove it: 0,99999... = sum(9*10^(-i)) = 9 * sum(10^(-i)) which is a geometric series equals to 9 * (1 / (10 - 1)) = 1
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There is a problem with infinite decimal numbers :
0,9999... * 10 = 9,9999..., but it is harder to prove than we can think.
But still, 0,999... = 1 and there is another way to proove it:
0,99999... = sum(9*10^(-i)) = 9 * sum(10^(-i))
which is a geometric series equals to 9 * (1 / (10 - 1)) = 1
(Cf. http://en.wikipedia.org/wiki/Geometric_series#Formula)