Definition:Successor
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Disambiguation
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Successor may refer to:
- Successor element: In an ordered set $\left({S, \preceq}\right)$, $a$ is a successor element to $b$ if and only if $b \prec a$.
- Immediate successor element: In an ordered set $\left({S, \preceq}\right)$, $a$ is the immediate successor element to $b$ if and only if $b \prec a$ and $\nexists c \in S: b \prec c \prec a$.
- Successor set: If $S$ is a set, then its successor set $S^+$ is defined as $S^+ := S \cup \left\{{S}\right\}$.
- Successor mapping: The mapping at the heart of a Peano structure which encapsulates its ability to sustain the Principle of Mathematical Induction.
- Successor ordinal: An ordinal which is the successor set of some other ordinal.