ABSTRACT
Definition 21.1. A sequence in a set A is a map F : N → A. If we write F (n) = an we also say that a1, a2, ... is a sequence in A or that (an) is a sequence in A.
Theorem 21.2. (Recursion theorem) Let A be a set, a ∈ A an element, and let F1, F2, ... be a sequence of maps A→ A. Then there is a unique map G : N→ A such that F (1) = a and G(n+ 1) = Fn(G(n)) for all n ∈ N.
