 Such definitions may thus be understood to provide algorithms for computing the values of the functions so  defined.[20]  For observe that each natural number \(n\) is either equal to 0 or is of the form \(m+1\) for some \(m \in \mathbb{N}\). If we now introduce the abbreviation \(\overline{n} = s(s(s \ldots (s(\mathbf{0}))))\) \(n\)-times, the result of applying the successor function \(s\) to a number denoted by \(\overline{n}\) thus yields the number denoted by \(\overline{n+1}\). We may thus compute the value of \(x + y\) using the prior recursive definition of addition as follows: