Definition:Precede

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Definition

Let $\left({S, \preceq}\right)$ be an ordered set.

Let $a, b \in S$ such that $a \preceq b$.


Then $a$ precedes $b$.


Also known as

The statement $b$ precedes $a$ can be expressed as $b$ is a predecessor of $a$.


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


When the underlying set $S$ of the ordered set $\left({S, \leqslant}\right)$ is one of the sets of numbers $\N$, $\Z$, $\Q$, $\R$ or a subset, the term is less than or equal to is usually used instead of precedes.


Also defined as

Some sources use the term predecessor to mean immediate predecessor.


Also see


Sources