 A simple example, again from standard mathematics, is the interpretation of the group \(\mathbb{Z}\) of integers in the structure \(\mathbb{N}\) consisting of the natural numbers 0, 1, 2 etc. with labels for 0, 1 and +. To construct the domain of \(\mathbb{Z}\) we first take the set \(X\) of all ordered pairs of natural numbers (clearly a definable relation in \(\mathbb{N})\), and on this set \(X\) we define the equivalence relation \(\sim\) by