Every ordinal no relation limit ordinal
In set theory, the successor of an ordinal number α is the smallest ordinal number greater than α.  An ordinal number that is a successor is called a successor ordinal.Properties
Every ordinal other than 0 is either a successor ordinal or a limit ordinal.In Von Neumann's model
Using 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
no relation