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Given the equation $$\lvert2x\rvert=x-1,$$ rewriting the left-hand side as $\pm2x$ results in the unique solution set $\{-1,\frac13\},$ which nevertheless fails to satisfy the equation. (The equation has extraneous but no actual solutions.)


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I really like the idea of discovery fictions because they capture an essential component of how mathematics is best understood and communicated. Almost all ideas in mathematics follow simply and inexorably from previous ideas, and understanding any mathematical discipline consists almost entirely of figuring out how you could have developed these ideas on ...


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A. CIT is (in)famous for having a freshman calculus course, with substantial analysis content. http://www.math.caltech.edu/~2014-15/1term/ma001a/ The course is not supersized in terms of credit size though. And it presupposes AP5 level of capability for the incoming students. And the kids hate it. B. For various reasons, I think the suggestion to mix ...


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