ntrianglelefteq

Represents the mathematical relation 'not left triangle equal to', indicating that one value is not less than or equal to another in a specific partial ordering.

Overview

Serves as a negation of the trianglelefteq relation, commonly used in advanced mathematics and formal logic to express order relationships and set comparisons.

Essential in order theory and abstract algebra for describing non-containment or non-dominance.
Frequently appears in proofs and formal mathematical writing where precise ordering relationships need to be negated.
Particularly useful in lattice theory and when working with partially ordered sets.
Often paired with similar ordering symbols to express complex mathematical relationships.

Examples

Expressing that a sequence is not monotonically decreasing.

a_n \ntrianglelefteq a_{n+1}

a_n \ntrianglelefteq a_{n+1}

Showing a non-dominated relationship between sets.

A \ntrianglelefteq B \implies A \not\subset B

A \ntrianglelefteq B \implies A \not\subset B

Denoting non-precedence in a partial order relation.

x \ntrianglelefteq y \quad \text{and} \quad y \ntrianglelefteq x

x \ntrianglelefteq y \quad \text{and} \quad y \ntrianglelefteq x