It is an upper bound on the growth. But _what_ you're upper bounding is not specified. Big-O notation works on mathematical functions. In the usual case, the f

It is an upper bound on the growth. But _what_ you're upper bounding is not specified. Big-O notation works on mathematical functions. In the usual case, the function you're upper bounding is the worst-case run time of a procedure for a given input size. But that's _far_ from the only case.