TeXipedia

lrarr

Represents a bidirectional horizontal arrow indicating equivalence, mutual implication, or two-way correspondence between mathematical expressions.

Overview

Essential for expressing logical equivalence, mutual relationships, and reversible processes in mathematical notation and formal proofs.

  • Common in mathematical logic to denote logical equivalence or biconditional statements
  • Used in set theory to show bijective mappings between sets
  • Appears in physics and chemistry to indicate reversible reactions or processes
  • Helpful in computer science for expressing bidirectional data flow or mutual dependencies

Examples

Showing logical equivalence between two mathematical statements.

p∧q↔q∧pp \land q \lrarr q \land p 
p \land q \lrarr q \land p

Expressing a bidirectional implication in set theory.

x∈A∪B↔x∈A or x∈Bx \in A \cup B \lrarr x \in A \text{ or } x \in B 
x \in A \cup B \lrarr x \in A \text{ or } x \in B

Demonstrating equality of complex expressions.

∣z1z2∣↔∣z1∣∣z2∣\left|z_1z_2\right| \lrarr \left|z_1\right|\left|z_2\right| 
\left|z_1z_2\right| \lrarr \left|z_1\right|\left|z_2\right|