Definition:Succeed

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

• Definition:Strictly Succeed
• Definition:Immediate Successor Element

• Definition:Precede

• Results about successor elements can be found here.