Growth of Functions

The notation used to describe the asymptotic running time of an algorithm is defined in terms of functions whose domains are the set of natural numbers. This notation refers to how the problem scales as the problem gets larger. In some cases it is important to look at how fast the problem is for small amounts of input, particularly when the same task is being done over and over again. However, we are mainly concerned with algorithms for large problems, hence how the performance scales as the problem size approaches infinity is what we will look at.