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ChristianKl comments on Welcome to Less Wrong! (7th thread, December 2014) - Less Wrong
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And current mathematician have them with infinitesimally small numbers ;)
I don't think modern mathematicians are going to drown someone for using infinitesimally small numbers...
Not really. Everyone agrees that calculus can be done with infinitesimals, but most mathematicians think that doing it with limits forms a better basis for going on to real analysis and epsilon-delta proofs later.
Non-standard analysis is perfectly fine. Most mathematicians just don't deal with that kind of analysis.