TeXipedia

Harr

Represents a double-headed horizontal arrow with thick lines, commonly used to indicate logical equivalence or bidirectional implications.

Overview

Serves as a prominent notation in mathematical logic, set theory, and formal proofs where bidirectional relationships need to be emphasized.

  • Essential in mathematical proofs to denote "if and only if" statements
  • Used in formal specifications and computer science to indicate mutual dependencies
  • Appears in set theory to show bijective mappings between sets
  • Common in textbooks and academic papers where logical equivalences need clear visual distinction from single implications

Examples

Logical equivalence in mathematical logic, showing two statements are equivalent.

p∧q⇔q∧pp \land q \Harr q \land p 
p \land q \Harr q \land p

Expressing a bidirectional implication between two mathematical expressions.

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

Showing equivalence between set definitions.

A⊆B⇔∀x(x∈A→x∈B)A \subseteq B \Harr \forall x(x \in A \rightarrow x \in B) 
A \subseteq B \Harr \forall x(x \in A \rightarrow x \in B)