Re:Controversial Facts In Mathematics
by alok-g on Wednesday March 27, 2013 @06:29PM
(#5452388)
Other than pointing to the Wikipedia article (thanks for the same), you have not said anything that I did not. The repetition of the decimals before the ellipsis is the same as the geometric series representation I mentioned. The Wikipedia article also mentions the limit in one of the proofs (though I am yet to read the other proofs there, which may be illuminating! :-)
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Mathematics isn't politics or law. The point is to come to a consensus on the meaning of symbols and conventions. The consensus is that the ellipsis in 0.999... extends out to infinity.
In mathematics, there is every incentive to agree on axioms like the meaning of the ellipsis. In science, there is every incentive to agree on the meaning of evidence and how it relates to theory. Only in psychology do they vote on the meaning of their "scientific" findings (all the new conditions that made their way into the new DSM got there by votes, not evidence) -- but psychology isn't a science, it's a pseudoscience.
Meanwhile, based on the agreed-upon axioms, 0.999... is equal to 1.