Definition:Successor
From ProofWiki
Disambiguation
This page lists articles associated with the same title.
If an internal link led you here, you may wish to change the link to point directly to the intended article.
Successor may refer to:
- Successor element: In a poset $\left({S, \preceq}\right)$, $a$ is a successor element to $b$ iff $b \prec a$.
- Immediate successor element: In a poset $\left({S, \preceq}\right)$, $a$ is the immediate successor element to $b$ iff $b \prec a$ 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 Finite Induction.
- Successor ordinal: An ordinal which is the successor set of some other ordinal.
