Definition:Succeed

Definition
Let $\left({S, \preceq}\right)$ be a poset.

Let $a, b \in S$ such that $a \preceq b$.

Then $b$ succeeds $a$.

Successor
If $a \preceq b$, then $b$ is a successor of $a$.

Beware: some sources use the term successor to mean immediate successor.

If it is important to make the distinction between a successor and a strict successor, the term weak successor can be used for successor.

Also see

 * Strictly succeed
 * Immediate Successor


 * Precede
 * Strictly precede
 * Immediate Predecessor