Why is O(f(n)) − O(f(n)) not equal to 0? Full disclosure this is a question from practice problems for my theory class.
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Getting down to the question, I'll leave you with a small hint. Big-O of f(n) denotes a class of functions that have a higher rate of growth than f(n) after a certain point. Hence, O(n^2) includes n, nlogn, n^2 and many more! It should be easy for you to get to the solution now.