Definition:Strictly Precede

Definition

Let $\left({S, \preceq}\right)$ be a poset.

Let $a \preceq b$ such that $a \ne b$.

Then $a$ strictly precedes $b$.

When $a \preceq b$ and $a \ne b$, it is usual to denote it $\prec$, with similarly derived symbols from other ordering symbols.

Strict Predecessor

If $a \prec b$, then $a$ is a (strict) predecessor of $b$.

Beware: some sources use the term predecessor to mean immediate predecessor.

Also see

• Strictly Precedes is a Strict Ordering

• Precede
• Immediate Predecessor Element

• Succeed
• Strictly Succeed
• Immediate Successor Element

Sources

• Paul R. Halmos: Naive Set Theory (1960)... (previous)... (next): $\S 14$: Order