Question: Let h : |0, 1| R be a function that takes on each of its values exactly twice. Show that h cannot be continuous

Let h : |0, 1| → R be a function that takes on each of its values exactly twice. Show that h cannot be continuous at every point. [If c1 < c2 are the points where h attains its supremum, show that c1 = 0, c2 = 1. Now examine the points where h attains its infimum.]

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