Stew Posted April 3, 2009 Share Posted April 3, 2009 Suppose .9999999999 (repeating) is not equal to 1.Then these are two distinct numbers, call them x and z. Then there exists a y such that x + y = z. i.e. (by the additive inverse property). So since x = .99999999 repeating, y = .00000000000 repeating and finally a 1. How many 0's are there? If there are finitely many 0's (say n) then y = 10^-n. This contradicts that x has infinitely many nonzero digits since x + 10^-n = z So y must have an infinite number of 0's before the 1. But if y has an infinite number of 0's then y = 0. Then it follows that x = y, i.e. .999999999 (repeating) equals 1. This does make sense though, Im going with Im not sure anymore..... :laugh: Link to comment Share on other sites More sharing options...
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