Definition:Strictly Precede

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

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.

Also known as
Some sources refer to a strict predecessor simply as a predecessor.

Also see

 * Strictly Precedes is Strict Ordering


 * Precede
 * Immediate Predecessor Element


 * Succeed
 * Strictly Succeed