seeing more math on the TL recently. i haven't mathposted in a long time but i'm still happy to field math questions from twitter peeps, just reply here or tag me or w/e. big meaty philosophical questions like "wtf are real numbers anyway" would be particularly fun for me rn
Conversation
Why are there several different types of integrals and what are the useful differences between these?
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the riemann integral is traditional and relatively straightforward to define. the traditional approach to the lebesgue integral requires some truly tedious preliminaries (setting up measure theory is a gigantic pain in the ass) but results in an integral with nicer theorems
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i’ve never used the henstock-kurzweil integral. supposedly it is even nicer than the lebesgue integral but the lebesgue integral makes sense in much greater generality. it seems very niche