Definition:Successor Mapping/Successor Set

Definition
Let $S$ be a set.

The successor (set) of $S$ is defined and denoted:
 * $S^+ := S \cup \left\{{S}\right\}$

Alternative notation
Some sources use $S'$ rather than $S^+$.

Some sources use $S + 1$ rather than $S^+$, on the grounds that they mean the same thing when applied to the set of natural numbers.

Some sources call this the Halmos function, for Paul R. Halmos who made extensive use of it in his 1960 work.