What ciphergoth said. Or to put it another way, "0.9..." or "0.9 recurring" [*] has a specific mathematic definition (an infinite sum), but "0.0...1" does not - and whenever I ask such a person for its definition, they are unable to provide one.
(Just to clarify - I don't mean to mock people who don't see that 0.9recurring = 1 - after all, the rigorous proof is rather high level, and the "simple proofs" aren't really rigorous. I mean more that the issue tends to attract some people who insist they are right, but are unable to either justify it, or find a fault in the proof that shows they are equal. I think it's a bit like the evolution of the mathematical world, except not with all the political and religious dispute.)
[*] I think one of the points that causes misunderstanding is the use of "...", which probably gets misunderstood as simply meaning "a lot of 9s". I'd prefer to use the notation of putting a dot or bar over the 9, but of course that's not so easy when writing online...
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timeasmymeasure
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Date: 2009-02-20 10:48 am (UTC)(Just to clarify - I don't mean to mock people who don't see that 0.9recurring = 1 - after all, the rigorous proof is rather high level, and the "simple proofs" aren't really rigorous. I mean more that the issue tends to attract some people who insist they are right, but are unable to either justify it, or find a fault in the proof that shows they are equal. I think it's a bit like the evolution of the mathematical world, except not with all the political and religious dispute.)
[*] I think one of the points that causes misunderstanding is the use of "...", which probably gets misunderstood as simply meaning "a lot of 9s". I'd prefer to use the notation of putting a dot or bar over the 9, but of course that's not so easy when writing online...