Every mathematical object may be viewed as a set. For example, the natural numbers are identified with the finite ordinals, so \(\mathbb{N}=\omega\). The set of integers \(\mathbb{Z}\) may be defined as the set of equivalence classes of pairs of natural numbers under the equivalence relation \((n, m)\equiv (n',m')\) if and only if \(n+m'=m+n'\). By identifying every natural number \(n\) with the equivalence class of the pair \((n,0)\), one may extend naturally the operations of sum and product of natural numbers to \(\mathbb{Z}\) (see Enderton (1977) for details, and Levy (1979) for a different construction). Further, one may define the rationals \(\mathbb{Q}\) as the set of equivalence classes of pairs \((n,m)\) of integers, where \(m\ne 0\), under the equivalence relation \((n,m)\equiv (n',m')\) if and only if \(n\cdot m'=m\cdot n'\). Again, the operations \(+\) and \(\cdot\) on \(\mathbb{Z}\) may be extended naturally to \(\mathbb{Q}\). Moreover, the ordering \(\leq_{\mathbb{Q}}\) on the rationals is given by: \(r \leq_{\mathbb{Q}} s\) if and only if there exists \(t\in \mathbb{Q}\) such that \(s=r+t\). The real numbers may be defined as Dedekind cuts of \(\mathbb{Q}\), namely, a real number is given by a pair \((A,B)\) of non-empty disjoint sets such that \(A\cup B=\mathbb{Q}\), and \(a\leq_{\mathbb{Q}}b\) for every \(a\in A\) and \(b\in B\). One can then extend again the operations of \(+\) and \(\cdot\) on \(\mathbb{Q}\), as well as the ordering \(\leq_{\mathbb{Q}}\), to the set of real numbers \(\mathbb{R}\).