TeXipedia

smallsetminus

Represents set difference or relative complement in set theory with a smaller, more elegant notation than the standard setminus.

Overview

Provides a refined alternative to the standard setminus symbol, particularly valued in mathematical writing where aesthetic presentation matters.

  • Commonly used in advanced mathematics and set theory to denote A\B (elements in A that are not in B)
  • Preferred in professional typesetting due to its more proportional size and cleaner appearance
  • Especially useful in expressions with multiple set operations where the standard setminus might appear too dominant
  • Popular in academic papers and textbooks focusing on set theory, topology, and abstract algebra

Examples

Showing the difference between two sets A and B.

A∖B={x∈A:x∉B}A \smallsetminus B = \{x \in A : x \notin B\} 
A \smallsetminus B = \{x \in A : x \notin B\}

Expressing the complement of a subset.

X∖Y⊆XX \smallsetminus Y \subseteq X 
X \smallsetminus Y \subseteq X

Defining a set by excluding specific elements.

R∖{0}\mathbb{R} \smallsetminus \{0\} 
\mathbb{R} \smallsetminus \{0\}