An example of a function is formula_7. One gives a natural number formula_8 (0,1,2,3...) as the input, and gets a natural number formula_9, which is formula_8 +1 (1,2,3,4...) The idea of a function has been set up to cover all sorts of possibilities. The function doesn't have to be an equation. The main idea is that inputs and outputs are paired up somehow—even if the process might be very complicated.