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Big O notation is an effective way to measure how quickly things grow. In class we discuss the definition that big O notation is an equivalence relation of functions from R+ to R+ defined by O(f) = O(g) if limx f(x)/g(X) = C R+ We say that f is polynomial complexity if there exists an n N with O(f) O(xn) and we say that it is exponential complexity if there exist real numbers ab both greater than 1 with O(ax) O(f) O(bx). Give an example of a function g with O(g) > O(f) for every polynomial complexity function but O(g) < O(f) for every exponential complexity function.