January 2014 Archives

In the previous post I discussed the foundations of the differential calculus. Initially defined in the 17th century in terms of the rather vaguely defined infinitesimals, it was not until the 19th century that Cauchy gave it a rigorous definition with his formalisation of the concept of a limit. Fortunately for us, the infinitesimals were given a solid footing in the 20th century with Conway’s surreal numbers and Robinson’s non-standard numbers, saving us from the annoyingly complex reasoning that Cauchy’s approach requires.

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