# Definition:Strictly Succeed

(Redirected from Definition:Strict Successor)

## Definition

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

Let $a \prec b$.

That is, let $a$ strictly precede $b$.

Then $b$ strictly succeeds $a$.

This can be expressed symbolically as:

$b \succ a$

## Also known as

The statement $b$ strictly succeeds $a$ can be expressed as $a$ is a strict succcessor of $b$.

Some sources refer to a strict successor simply as a successor.

Some sources say that $b$ follows $a$.

When the underlying set $S$ of the ordered set $\left({S, <}\right)$ is one of the sets of numbers $\N$, $\Z$, $\Q$, $\R$ or a subset, the term is greater than is usually used instead of (strictly) succeeds.