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From what I read on the subject, this _was_ the main way of dealing with calculus, but it was not rigorous. The first rigorous definition of a limit was given u
by iib 5y ago
From what I read on the subject, this _was_ the main way of dealing with calculus, but it was not rigorous. The first rigorous definition of a limit was given using the epsilon-delta approach, by Weierstrass, with of course many many contributions by his predecessors.
Everybody switched during the 19th century, because epsilon-delta was in fact the only rigorous method.
Abraham Robinson gave a rigorous foundation for infinitesimals only in 1960.
- chithanh 5y agoWork done by Schmieden&Laugwitz in the 1950s helped to formalize and retroactively apply rigor to the earlier uses of infinitesimals. Their Omega Calculus approach was also constructive. cf. Detlef Laugwitz, Curt Schmieden's Approach to Infinitesimals. https://doi.org/10.1007/978-94-015-9757-9_12 https://doi.org/10.1007/978-94-015-9757-9_12 However this turned out less useful going forward.