6 Moving from one set to another - Functions

In mathematics, we are very often concerned with functions (also called maps). Some functions model the behaviour of complex systems, while other functions allow us to compare two sets. Loosely speaking, a function is a black box which takes an input from one set and gives an output in another. Every input must have an output, and there is no randomness, so the same input always gives the same output. To give a formal definition of functions, we need to go back to sets.