Definition:Successor Mapping/Successor Set

Definition
Let $S$ be a set.

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

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

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.

Also see

 * Minimal Infinite Successor Set


 * Natural Numbers are Elements of Minimal Infinite Successor Set