Definition:Succeed/Also known as

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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.