TeXipedia

frown

Represents a downward-curved relation symbol commonly used in mathematical notation and set theory.

Overview

Serves as a binary relation operator in mathematical expressions, particularly useful in abstract algebra and formal logic. The curved shape visually indicates a specific type of relationship between elements.

  • Frequently used in advanced mathematics to denote specialized relations
  • Often appears alongside other relation symbols like \smile in formal proofs
  • Common in set theory and abstract algebraic structures
  • Useful for expressing certain topological or geometric relationships

Examples

Expressing a binary relation 'frowns upon' in mathematical logic.

A⌢BA \frown B 
A \frown B

Denoting a non-compatibility relation between elements.

x⌢y  ⟹  x≠yx \frown y \implies x \neq y 
x \frown y \implies x \neq y

Representing an opposing or inverse relationship in set theory.

{(a,b):a⌢b}⊆X×Y\{(a,b) : a \frown b\} \subseteq X \times Y 
\{(a,b) : a \frown b\} \subseteq X \times Y