Definition:Strictly Succeed
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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