Definition:Strictly Precede/Definition 1
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Definition
Let $\struct {S, \prec}$ be a strictly ordered set.
Let $a, b \in S$ and $a \prec b$.
Then $a$ strictly precedes $b$.
Notation
When $a \preceq b$ and $a \ne b$, it is usual to denote this with the symbol:
- $a \prec b$
and similar derived notation for other ordering symbols.
Also known as
The statement $a$ strictly precedes $b$ can be expressed as $a$ is a strict predecessor of $b$.
Some sources refer to a strict predecessor simply as a predecessor.
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 less than is usually used instead of (strictly) precedes.
Sources
- 1955: John L. Kelley: General Topology ... (previous) ... (next): Chapter $0$: Orderings