TeXipedia

hArr

Represents a double-headed horizontal arrow indicating logical equivalence or bidirectional implication in mathematical notation.

Overview

Essential in mathematical logic, set theory, and formal proofs where bidirectional relationships or equivalences need to be expressed clearly.

  • Commonly used to show if and only if (iff) relationships in logical statements
  • Appears frequently in mathematical definitions where two statements are mutually equivalent
  • Useful in computer science for expressing bidirectional mappings or transformations
  • Often employed in abstract algebra to denote isomorphisms between structures

Examples

Logical equivalence in a mathematical statement

p∧q⇔rp \land q \hArr r 
p \land q \hArr r

Showing bidirectional implication between expressions

x2=4⇔x=±2x^2 = 4 \hArr x = \pm 2 
x^2 = 4 \hArr x = \pm 2

Indicating a two-way relationship in set theory

A⊆B and B⊆A⇔A=BA \subseteq B \text{ and } B \subseteq A \hArr A = B 
A \subseteq B \text{ and } B \subseteq A \hArr A = B