In ZFC one can develop the Cantorian theory of transfinite (i.e., infinite) ordinal and cardinal numbers. Following the definition given by Von Neumann in the early 1920s, the ordinal numbers, or ordinals, for short, are obtained by starting with the empty set and performing two operations: taking the immediate successor, and passing to the limit. Thus, the first ordinal number is \({\varnothing}\). Given an ordinal \(\alpha\), its immediate successor, denoted by \(\alpha +1\), is the set \(\alpha \cup \{ \alpha \}\). And given a non-empty set \(X\) of ordinals such that for every \(\alpha \in X\) the successor \(\alpha +1\) is also in \(X\), one obtains the limit ordinal \(\bigcup X\). One shows that every ordinal is (strictly) well-ordered by \(\in\), i.e., it is linearly ordered by \(\in\) and there is no infinite \(\in\)-descending sequence. Also, every well-ordered set is isomorphic to a unique ordinal, called its order-type.