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Proving 0.999… Is Equal To 1

October 14th, 2010 10:34 admin Leave a comment Go to comments

eldavojohn writes “Some of the juiciest parts of mathematics are the really simple statements that cause one to immediately pause and exclaim “that can’t be right!” But a recent 28 page paper in The Montana Mathematics Enthusiast (PDF) spends a great deal of time fielding questions by researchers who have explored this in depth and this seemingly impossibility is further explored in a brief history by Dev Gualtieri who presents the digit manipulation proof: Let a = 0.999… then we can multiply both sides by ten yielding 10a = 9.999… then subtracting a (which is 0.999…) from both sides we get 10a — a = 9.999… — 0.999… which reduces to 9a = 9 and thus a = 1. Mathematicians as far back as Euler have used various means to prove 0.999… = 1.”

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