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Let f: [a, b] → [a, b] be continuous. A fixed point of f is a member x E [a, b] such that x = f(x). Prove that f has at least one fixed point.

Let f: [a, b] → [a, b] be continuous. A fixed point of f is a member x E [a, b] such that x = f(x). Prove that f has at least one fixed point.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.5: Permutations And Inverses
Problem 10E: 10. Let and be mappings from to. Prove that if is invertible, then is onto and is...
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Let f:[a, b] → [a, b] be continuous. A fixed point of f is a member x E [a, b] such that x = f(x). Prove that f has at least one fixed point.
Transcribed Image Text:Let f:[a, b] → [a, b] be continuous. A fixed point of f is a member x E [a, b] such that x = f(x). Prove that f has at least one fixed point.
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