Over on mathoverflow, there is a popular CW question titled: Examples of common false beliefs in mathematics. I thought it would be nice to have a parallel question on this site to serve as a reference for false beliefs within less obscure mathematics. That said, it would be good not get bogged down with misconceptions that are generally assumed to be elementary such as: $(x + y)^{2} = x^{2} + y^{2}$.
False beliefs in mathematics (conceptual errors made despite, or because of, mathematical education)
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19I dont really see a need for this question. :/ I think the one on Mathoverflow is welcoming of examples in other areas of math rather than "obscure". I think that it is a cool question, but I really dont think we need this duplicate. – 2010-10-26
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0http://math.stackexchange.com/questions/6848/finding-lim-x-to-0-frac-sin-cosx-secx this is another instance. – 2010-10-26
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0@BBischof: I agree with you as well. There are lots of answers in MO, some of them which are elementary in nature as well – 2010-10-26
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5Voted to close. This is a dup, as per the question itself. – 2010-10-26
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0The MO question had a narrower scope that made it interesting. Is there a difference between this version of the question and "list all possible conceptual errors in elementary mathematics"? – 2010-10-26
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4Specifically, the MO discussion focused on mistakes that were (a) conceptual, and (b) known to be made by mathematicians (especially, mistakes the answerers had made). This restriction prevented trivial responses. I suggest revising the question to be "false beliefs YOU -- a presumably mathematically capable math.SE user -- have held" as a separate matter from "review every error that students make!". If the latter is interesting it would be better to explore it in another thread. – 2010-10-26
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1@T.. Title has been edited as per your suggestion. – 2010-10-26
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0It is a little awkward as a title (I meant the text of the question!) but I edited it. Maybe someone else has a better title for this. – 2010-10-26
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0You may want to read the following from David Mumford about the Italian school of Algebraic Geometry: http://ftp.mcs.anl.gov/pub/qed/archive/209. – 2013-06-18