4 ms·
They are well-defined, but the usual framework that explains them ("non-standard analysis") is extremely abstract. If you are dealing with polynomials/algebrai
by galimaufry 7y ago
They are well-defined, but the usual framework that explains them ("non-standard analysis") is extremely abstract.
If you are dealing with polynomials/algebraic geometry only then there is a very simple, totally rigorous approach using nilpotents. And there is a newer approach called "alpha calculus" that I know nothing about but here is an example: https://arxiv.org/pdf/0807.3477.pdf https://arxiv.org/pdf/0807.3477.pdf
- jordigh 7y agoThey are well-defined now, but when Leibniz and Cauchy were working with them, they were not, and used carelessly could lead to errors. Their "solution" was to just pretend those errors didn't happen ("don't do that, then") instead of trying to come up with a consistent system of rules for infinitesimals.