Definition:Strictly Succeed

Definition

Let $\struct {S, \preceq}$ 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 successor 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 $\struct {S, <}$ 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.

Also see

• Strictly Succeeds is Strict Ordering

• Definition:Succeed
• Definition:Immediate Successor Element

• Definition:Precede
• Definition:Strictly Precede

Sources

• 1955: John L. Kelley: General Topology ... (previous) ... (next): Chapter $0$: Orderings