precneqq
Denotes a strict precedence relationship that is explicitly not equal, commonly used in order theory and mathematical logic.
Overview
Serves as a specialized relational operator in mathematical contexts where precise ordering relationships need to be explicitly distinguished from equality. This symbol combines the concepts of precedence and inequality into a single notation.
- Essential in formal mathematics and theoretical computer science for expressing strict ordering relationships
- Particularly useful in order theory when describing partially ordered sets
- Often appears alongside similar relations in formal proofs and mathematical definitions
- Helps mathematicians express nuanced relationships between elements where both precedence and non-equality need emphasis
Examples
Comparing two sequences where one strictly precedes another.
\{1,2,3\} \precneqq \{1,2,3,4\}Expressing strict precedence between partially ordered sets.
A \precneqq B \implies |A| < |B|Showing proper subset relationship with additional order properties.
P_n \precneqq P_{n+1} \precneqq P_{n+2}