 Proof: It is a simple consequence of the definition of ‘weak ancestral’ that \(R^{+}\) is reflexive (see Fact 4 about \(R^{+}\) in our subsection on the Weak Ancestral in §4). So \(\mathit{Precedes}^{+}(0,0)\). Hence, by the definition of natural number, \(0\) is a natural number.