npreceq
Represents a negated precedes-or-equals relation in mathematical notation, commonly used in order theory and set comparisons.
Overview
Serves as a fundamental symbol in advanced mathematics for denoting strict ordering relationships, particularly when expressing that one element does not precede or equal another in a partially ordered set.
- Essential in order theory and abstract algebra for expressing non-precedence relationships
- Frequently used in proofs and formal mathematical writing to establish strict inequalities
- Appears in set theory when describing relationships between ordered pairs or sequences
- Commonly combined with other ordering symbols to express complex mathematical relationships
Examples
Expressing that one sequence is not weakly dominated by another sequence.
\{a_n\} \npreceq \{b_n\}Showing a partial order relation does not hold between sets.
A \npreceq B \implies |A| > |B|Demonstrating inequality in operator theory.
T_1 \npreceq T_2 \text{ on } L^2(\mathbb{R})