A metric space is complete if every sequence named for this mathematician converges. For 10 points each:
[10m] Name this French mathematician, who also names an inequality bounding the inner product of two vectors with Hermann Schwarz (“sh’VARTS”).
ANSWER: Augustin-Louis Cauchy (“ko-SHEE”) [accept Cauchy sequences; accept Cauchy-Schwarz inequality]
[10e] If a complex function satisfies the Cauchy-Riemann equations, then a form of this operation can be performed on it. Integration is the inverse of this operation.
ANSWER: differentiation [or word forms such as differentiating; or taking the derivative; accept complex differentiation or complex derivative; prompt on holomorphic or analytic or entire functions by asking “What operation can be performed on such a function?”]
[10h] Cauchy used the mean value theorem to prove this theorem, which states any differentiable function that takes the same value at two different points must have a stationary point between the two points.
ANSWER: Rolle’s theorem [or Rolle’s lemma]
<Other Science>