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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.

{an}{bn}\{a_n\} \npreceq \{b_n\}
\{a_n\} \npreceq \{b_n\}

Showing a partial order relation does not hold between sets.

AB    A>BA \npreceq B \implies |A| > |B|
A \npreceq B \implies |A| > |B|

Demonstrating inequality in operator theory.

T1T2 on L2(R)T_1 \npreceq T_2 \text{ on } L^2(\mathbb{R})
T_1 \npreceq T_2 \text{ on } L^2(\mathbb{R})