lrArr

Represents a double-headed horizontal arrow indicating a bidirectional relationship or equivalence between mathematical expressions.

Overview

Commonly employed in mathematical logic, set theory, and formal proofs to denote logical equivalence, mutual implication, or reversible transformations.

Essential in mathematical reasoning to show if-and-only-if relationships
Frequently used in algebraic manipulations to indicate steps that can be reversed
Appears in computer science and discrete mathematics for showing bijective mappings
Useful in formal definitions and theorem statements where bidirectional implications are crucial

Examples

Logical equivalence in a mathematical statement

p \land q \lrArr r

p \land q \lrArr r

Showing bidirectional implication between expressions

x^2 = 4 \lrArr x = \pm 2

x^2 = 4 \lrArr x = \pm 2

Demonstrating equivalence of mathematical definitions

f\text{ is continuous} \lrArr \lim_{x \to a} f(x) = f(a)

f\text{ is continuous} \lrArr \lim_{x \to a} f(x) = f(a)