TeXipedia

smallfrown

Represents a small downward-curved arc or frown symbol commonly used in mathematical notation and relational expressions.

Overview

Serves as a compact relational operator in mathematical expressions, particularly useful in abstract algebra, set theory, and formal logic.

  • Often employed to denote specific mathematical relations or mappings
  • Provides a visually distinct alternative to standard relation symbols
  • Frequently appears in advanced mathematical texts and academic papers where precise notation is essential
  • Particularly useful when multiple distinct relation symbols are needed within the same context

Examples

Expressing a negative relation between two variables in set theory.

x⌢yx \smallfrown y 
x \smallfrown y

Showing non-compatibility between elements in abstract algebra.

a1⌢a2a_1 \smallfrown a_2 
a_1 \smallfrown a_2

Denoting an inverse relation in mathematical logic.

P(x)⌢Q(x)P(x) \smallfrown Q(x) 
P(x) \smallfrown Q(x)