# Definition:Succeed

(Redirected from Definition:Successor Element)

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## Definition

Let $\preceq$ be an ordering.

Let $a, b$ be such that $a \preceq b$.

Then **$b$ succeeds $a$**.

$a$ is then described as being a **successor** of $b$.

## Also known as

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

If it is important to make the distinction between a **succcessor** and a **strict successor**, the term **weak successor** can be used for **succcessor**.

When the underlying set $S$ of the ordered set $\struct {S, \leqslant}$ is one of the sets of numbers $\N$, $\Z$, $\Q$, $\R$ or a subset, the term **is greater than or equal to** is usually used instead of **succeeds**.

## Also defined as

Some sources use the term **successor** to mean immediate successor.

## Also see

- Results about
**successor elements**can be found here.