LITTLE o’S AND BIG O’S.
Suppose you have a function f (x) with f (a) = 0 and you want to consider how quickly the function goes to zero around a. Then ideally you would want to find a simple function g (for example g(x) = (x − a)n ) which also vanishes at a such that g and f are almost equal around a. The little o and big O notation, want to express something like that, but only state that f goes to zero faster than g. For error terms this is of course sufficient (you just want to know that the error term is small), so they are used mostly in that context. Definition 1. We say f (x) = O(g(x)) as
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