Here are two more. \paragraph*{Natural numbers} A function with domain $ \nat $ is usually called a sequence. A crucial property of $ \nat $ is that sequences can be defined recursively: given a set $ X $ , an element $ a \in X $ , and a function $ r{\colon}\linebreak[0] X \to X $ , there is a unique sequence $ (x_n)_{n = 0}^\infty $ of elements of $ X $ such that