# Definition:Successor Mapping/Successor Set

(Redirected from Definition:Successor Set)

## Definition

Let $V$ be a basic universe.

Let $s: V \to V$ denote the successor mapping on $V$.

For $x \in V$, the result of applying the successor mapping on $x$ is denoted $x^+$:

$x^+ := \map s x = x \cup \set x$

$x^+$ is referred to as the successor (set) of $x$.

## Also see

• Results about the successor mapping can be found here.