Definition:Succeed
Definition
Let $\left({S, \preceq}\right)$ be an ordered set.
Let $a, b \in S$ such that $a \preceq b$.
Then $b$ succeeds $a$.
Also known as
The statement $b$ succeeds $a$ can be expressed as $b$ is a succcessor of $a$.
If it is important to make the distinction between a successor and a strict successor, the term weak successor can be used for successor.
When the underlying set $S$ of the ordered set $\left({S, \leqslant}\right)$ is one of the sets of numbers $\N$, $\Z$, $\Q$, $\R$ or a subset, the term is greater than or equal to is usually used instead of succeeds.
Also defined as
Some sources use the term successor to mean immediate successor.
