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Heh heh, pages upon pages of people going No... NO! Aaaaaagh you're all wrong shut up about the .999... thing. This is worse/more amusing than the time that the Monty Hall problem was AOTD.
I find it interesting that the text of the article actually predicts the belief-path the doubters take... when faced with simple and easily graspable proofs, they change their minds and state that obviously this means that the number system is broken.
I find it interesting that the text of the article actually predicts the belief-path the doubters take... when faced with simple and easily graspable proofs, they change their minds and state that obviously this means that the number system is broken.
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And like the Monte Hall problem, the failure of people to understand is really helped along by lousy pedagogy.
The Wikipedia article does a relatively good job of presenting the proof, but it would be far better if it started with a paragraph discussing multiple representations of numbers as a common occurence in all notational systems, so instead of seeming needlessly and pointlessly counter-intuitive when first introduced the equality of 0.999... and 1 would be presented to the reader as a previously unnoticed instance of a perfectly familiar and ordinary phenomenon.