TeXipedia

leftrightsquigarrow

Represents a bidirectional wavy arrow indicating a mutual relationship or equivalence between mathematical expressions.

Overview

Commonly employed in mathematical proofs and logical reasoning to show reversible transformations or two-way implications between statements. This notation is particularly useful in:

  • Abstract algebra for showing isomorphisms between structures
  • Logic for representing logical equivalence or mutual implication
  • Set theory for depicting bijective mappings
  • Computer science for indicating bidirectional data flow or transformations

Examples

Showing a bidirectional relationship or equivalence between mathematical expressions.

x2+y2=r2↭r=x2+y2x^2 + y^2 = r^2 \leftrightsquigarrow r = \sqrt{x^2 + y^2} 
x^2 + y^2 = r^2 \leftrightsquigarrow r = \sqrt{x^2 + y^2}

Indicating a reversible chemical reaction in equilibrium.

H2O(l)↭H++OH−\text{H}_2\text{O}(l) \leftrightsquigarrow \text{H}^+ + \text{OH}^- 
\text{H}_2\text{O}(l) \leftrightsquigarrow \text{H}^+ + \text{OH}^-

Representing a bijective mapping between sets.

f:A↭Bf: A \leftrightsquigarrow B 
f: A \leftrightsquigarrow B