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In mathematics and science, it’s often too difficult to get precise formulas for things, so often researchers just estimate the growth. For example, in a previous post on the Fibonacci sequence, we found that the Fibonacci numbers grow roughly exponentially; that is, they are close to an exponential function, but there is a tiny error term. Often, we don’t actually care about the exact formula but we just want an idea of how quickly something grows. In order to capture this vague notion precisely, we use asymptotic notation, which captures all the long-run information contained in the original function.