# Definition:Strictly Succeed

(Redirected from Definition:Strict Successor)

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## 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

## Sources

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