nrightarrow

Represents a negated right arrow, indicating that a relationship, mapping, or implication does not hold or is false.

Overview

Essential in mathematical logic, set theory, and abstract algebra for expressing negative relationships or failed implications between elements or statements.

Commonly used in proofs by contradiction
Appears in set theory to show elements are not mapped to each other
Useful in abstract algebra for demonstrating non-homomorphisms
Frequently encountered in theoretical computer science for expressing non-reducibility

Examples

Showing that a sequence does not converge to a limit.

x_n \nrightarrow L \text{ as } n \to \infty

x_n \nrightarrow L \text{ as } n \to \infty

Indicating that a function is not a homomorphism between algebraic structures.

f: G \nrightarrow H

f: G \nrightarrow H

Expressing that an implication does not hold in logic.

P \nrightarrow Q

P \nrightarrow Q