TeXipedia

smallsmile

Represents a small upward-curved arc symbol commonly used in mathematical relations and set theory.

Overview

Serves as a compact notation in mathematical expressions where a smaller version of the smile relation is needed, particularly in formal logic and abstract algebra.

  • Often used to denote specific binary relations or operators
  • Appears in advanced mathematics texts dealing with order theory
  • Provides a more subtle alternative to the standard smile relation
  • Frequently employed in conjunction with other relation symbols for expressing complex mathematical statements

Examples

Expressing a binary relation in abstract algebra.

R⌣SR \smallsmile S 
R \smallsmile S

Denoting a compatibility relation between elements.

x⌣yx \smallsmile y 
x \smallsmile y

Representing a positive or friendly relationship in social network theory.

v1⌣v2  ⟹  E(v1,v2)v_1 \smallsmile v_2 \implies E(v_1, v_2) 
v_1 \smallsmile v_2 \implies E(v_1, v_2)