Given f : R → R let O(f) be the set of functions g for which there exist

| August 30, 2017

Question
Given f : R → R let O(f) be the set of functions g for which there exist positive constants c,a ∈ R such that |g(x)| ≤ c|f(x)| for all x > a. Define a relation R on the set S of functions mapping from R to R by (g,h)∈R if and only if g−h∈O(f). Prove that R is an equivalence relation on S.

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