Definition:Succeed

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

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

Then $b$ succeeds $a$.

Also, $b$ is called a successor of $a$.

Also known as
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 defined as
Some sources use the term successor to mean immediate successor.

Also see

 * Definition:Strictly Succeed
 * Definition:Immediate Successor Element


 * Definition:Precede