 Ordinals are traditionally denoted by lower case Greek letters \(\alpha,\beta,\gamma,\delta,\ldots\) and the relation \(\in\) on ordinals is notated simply by \(&lt;\). If \(\beta \) is a successor ordinal, i.e., \(\beta\) is the successor of some (necessarily unique) ordinal \(\alpha\) we also denotes \(\beta\) by \(\alpha'\). Another important fact is that for any family of ordinals \(\alpha_i\) for \(i\in I\) (I some set) there is a smallest ordinal, denoted by \(\sup_{i\in I}\alpha_i\) that is bigger than every ordinal \(\alpha_i\).