Editing Successor ordinal (section)

==In Von Neumann's model==
Using [[Ordinal number#Von Neumann definition of ordinals|von Neumann's ordinal numbers]] (the standard model of the ordinals used in set theory), the successor ''S''(''α'') of an ordinal number ''α'' is given by the formula<ref name="cameron"/>

:<math>S(\alpha) = \alpha \cup \{\alpha\}.</math>

Since the ordering on the ordinal numbers is given by ''α''&nbsp;<&nbsp;''β'' if and only if ''α''&nbsp;∈&nbsp;''β'', it is immediate that there is no ordinal number between α and ''S''(''α''), and it is also clear that ''α''&nbsp;<&nbsp;''S''(''α'').