Re:Controversial Facts In Mathematics
by lutusp on Thursday March 28, 2013 @01:05AM
(#5453406)
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.
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.