ELEGANT Continuous Function PROOF!
If n ≥ 1 is a positive integer, and if f is a continuous real-valued function on the closed interval [0, 1], then we prove that
f(x + 1/n) = f(x)
for some value of x in [0, 1]. The proof is a beautiful application of the intermediate value theorem in calculus, combined with a clever trick. The video is designed for calculus students, and real analysis students, interested in math proofs and creative tricks in calculus. The problem is an exercise in "Calculus" by Michael Spivak.
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