Explanation of “proofs” to an exasperated calculus student.pic.twitter.com/2b458fAwwo
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in the opinion of most mathematicians. Various flavors of constructivists, intuitionists, finitists, etc. think it does have implications >
and you can’t legitimately do analysis with non-constructive reals, so the intermediate value theorem is actually false.
Or, in sum: no, if you demand a high enough standard of rigor, you can’t prove anything.
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