Definition:Predecessor Element

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

 * Precede
 * Strictly precede
 * Immediate Predecessor


 * Succeed
 * Successor Element
 * Strictly succeed
 * Immediate Successor