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Possible Duplicate:
Does .99999… = 1?

$\frac{1}{3} + \frac{1}{3} + \frac{1}{3} = \frac{3}{3} = 1$

but

$0.\overline{3} + 0.\overline{3} +0.\overline{3} = 0.\overline{9}$

Does that mean that $0.\overline{9} = 1$ ? Any proof?

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    @DouglasS.Stone: it doesn't really add anything to the discussion to note that$=$is an equivalence relation. It is true, but more to the point, it is that equivalence relation which allows one to substitute one expression for another. Properly used, equality *is* identity, in mathematics. To contemplate whether $0.\bar9$ *is* $1$, given that $0.\bar9$ *equals* $1$, is to introduce a distinction which doesn't exist (or at least, to make it evident that you need to define your terms clearly so that others can figure out what it is that you actually mean).2012-11-15

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