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by tmzt
4535 days ago
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Do you have any reference/proof/etc. for 0.999... === 1? As one of those taught to believe it is not, I would like to see it. Unfortunately, text books conserve non facts for very interesting reasons. Some good examples are at http://www.textbookleague.org/ |
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Let X = 0.999… Then 10X = 9.999…
10X - X = 9.999… - 0.999… = 9 = 9X Therefore X = 1.
Being able to do the subtraction infinitely is a little hand-wavy, but should suffice as a demo for middle and high schoolers.
More formal proofs involve limits that one wouldn't normally encounter until a course in real analysis.
Wikipedia has a whole page devoted to the topic: http://en.wikipedia.org/wiki/0.999...