 Infinite ordinals can be presented in naive set theory as isomorphism classes of well-orderings (a well-ordering is a linear order \(\le\) with the property that any nonempty subset of its domain has a \(\le\)-least element). We use reflexive, antisymmetric, transitive relations \(\le\) as our linear orders rather than the associated irreflexive, asymmetric, transitive relations \(\lt\), because this allows us to distinguish between the ordinal numbers 0 and 1 (Russell and Whitehead took the latter approach and were unable to define an ordinal number 1 in their Principia Mathematica).