Definition:Precede/Also known as

Definition
The statement $b$ precedes $a$ can be expressed as $b$ is a predecessor of $a$.

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

When the underlying set $S$ of the ordered set $\struct {S, \leqslant}$ is one of the sets of numbers $\N$, $\Z$, $\Q$, $\R$ or a subset, the term is less than or equal to is usually used instead of precedes.