Explanation of “proofs” to an exasperated calculus student.pic.twitter.com/2b458fAwwo
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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.
The point is not that math *should* be perfectly rigorous, it’s that teachers shouldn’t implicitly lie about the possibility of making it so
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