Lebl-Basic-Analysis-I · Problem 3.3.10

Continuous Functions

Mathematics · extreme-and-intermediate-value-theorems

Problem

Suppose f:[0,1]→[0,1]f : [0, 1] \to [0, 1] is continuous. Show that ff has a fixed point, in other words, show that there exists an x∈[0,1]x \in [0, 1] such that f(x)=xf(x) = x.

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