Definition:Precede

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

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

Then $a$ precedes $b$.

Predecessor
If $a \preceq b$, then $a$ is a predecessor (element) of $b$.

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

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 see

 * Strictly precede
 * Immediate Predecessor


 * Succeed
 * Strictly succeed
 * Immediate Successor