Definition:Precede

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

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

Then $a$ precedes $b$.

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

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

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

Also see

 * Definition:Strictly Precede
 * Definition:Immediate Predecessor Element


 * Succeed