TeXipedia

underleftrightarrow

Creates a bidirectional arrow underneath text or mathematical expressions, commonly used to indicate equivalence or correspondence between elements.

Overview

Serves as a specialized mathematical annotation tool, particularly valuable in advanced algebra, category theory, and theoretical mathematics where bidirectional relationships need to be emphasized.

  • Often employed to denote bijective mappings or one-to-one correspondences
  • Useful in showing transformations or relationships between mathematical objects
  • Frequently appears in advanced textbooks and research papers when describing isomorphisms or equivalences
  • Can be combined with other mathematical notation to create complex relationship indicators

Examples

Indicating a reversible chemical reaction between compounds A and B.

CH3COOHCH3COO+H+CH_3COOH \underleftrightarrow{} CH_3COO^- + H^+
CH_3COOH \underleftrightarrow{} CH_3COO^- + H^+

Showing a bidirectional mapping between two sets.

f:XYf: X \underleftrightarrow{} Y
f: X \underleftrightarrow{} Y

Representing a dynamic equilibrium in thermodynamics.

N2+3H22NH3N_2 + 3H_2 \underleftrightarrow{} 2NH_3
N_2 + 3H_2 \underleftrightarrow{} 2NH_3