Problem 1.1. Let f be a bijection from a finite set X to itself. Let f^2 denote f ∘ f and f^3 de

Name: Problem 1.1. Let f be a bijection from a finite set X to itself. Let f^2 denote f ∘ f and f^3 denote f ∘ f ∘ f, etc. Write f^-1 for the inverse function of f. Write f^-2 = f^-1∘ f^-1, f^-3 = f^-1∘ f^-1∘ f^-1, etc. Define f^0 = Id. Prove that f^a+b = f^a ∘ f^b for all integers a, b.
Uploaded: 2023-07-31T06:07:39-08:00
Duration: 2 min 38 s
Channel: Hoan Nguyen
Description: Problem 1.1. Let f be a bijection from a finite set X to itself. Let f^2 denote f ∘ f and f^3 denote f ∘ f ∘ f, etc. Write f^-1 for the inverse function of f. Write f^-2 = f^-1∘ f^-1, f^-3 = f^-1∘ f^-1∘ f^-1, etc. Define f^0 = Id. Prove that f^a+b = f^a ∘ f^b for all integers a, b.

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Step 1: We want to prove that fa+b = f" o fb for all integers a, b.

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