TeXipedia

harr

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

Overview

Essential for expressing logical equivalence, mutual implications, or two-way relationships in mathematical proofs and formal logic.

  • Common in mathematical logic to denote if-and-only-if statements
  • Used in set theory to show bijective mappings between sets
  • Appears frequently in computer science for expressing bidirectional data flows or transformations
  • Helpful in expressing reversible processes or symmetric relationships in various scientific contexts

Examples

Showing logical equivalence between two mathematical statements.

p∧q↔q∧pp \land q \harr q \land p 
p \land q \harr q \land p

Indicating a bidirectional mapping between sets.

f:A↔Bf: A \harr B 
f: A \harr B

Expressing if and only if relationship in a mathematical definition.

x is even↔x=2k for some k∈Zx \text{ is even} \harr x = 2k \text{ for some } k \in \mathbb{Z} 
x \text{ is even} \harr x = 2k \text{ for some } k \in \mathbb{Z}