Definition:Precede
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Definition
Let $\left({S, \preceq}\right)$ be a poset.
Let $a, b \in S$ such that $a \preceq b$.
Then $a$ precedes $b$.
Predecessor
If $a \preceq b$, then $a$ is a predecessor (element) of $b$.
Beware: some sources use the term predecessor to mean immediate predecessor.
If it is important to make the distinction between a predecessor and a strict predecessor, the term weak predecessor can be used for predecessor.
Also see
Sources
- Paul R. Halmos: Naive Set Theory (1960)... (previous)... (next): $\S 14$: Order
