Re:Calculus with Julia
by dan-robertson on Monday May 20, 2024 @11:18AM
(#40416492)
Ah thanks. My understanding was the whole epsilon-delta stuff one typically learns in a first course in analysis was due to Cauchy.
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No, epsilon-delta in the modern form was invented by Karl Weierstrass in 1861.
Cauchy's approach was to define an infinitesmal as a sequence approaching 0, and then to use the old infinitesmal definition of a derivative. This almost works. One of the places where it falls apart is defining the chain rule when the inner derivative is 0, because the sequence may wind up with 0/0 infinitely often.
But it is from this definition that we get Cauchy sequences today.