Definition:Strictly Precede/Definition 2

Definition
Let $\left({S, \preceq}\right)$ be an ordered set.

Let $a \preceq b$ such that $a \ne b$.

Then $a$ strictly precedes $b$.

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

When $a \preceq b$ and $a \ne b$, it is usual to denote this with:


 * $a \prec b$

and similar derived notation for other ordering symbols.

Equivalently, the $\prec$ relation is defined as the reflexive reduction of the $\preceq$ relation.