sqcup

Represents a binary operator denoting disjoint union, commonly used in set theory and abstract algebra.

Overview

Serves as a mathematical notation indicating the union of sets that are mutually disjoint (have no elements in common). This operator is particularly valuable in:

Set theory for combining collections while emphasizing their disjointness
Category theory when discussing coproducts
Abstract algebra for describing direct sums of algebraic structures
Topology when working with disjoint unions of topological spaces

Examples

Representing disjoint union of sets A and B.

A \sqcup B = \{x : x \in A \text{ or } x \in B\}

A \sqcup B = \{x : x \in A \text{ or } x \in B\}

Showing disjoint union of multiple indexed sets.

X = \bigsqcup_{i=1}^n X_i

X = \bigsqcup_{i=1}^n X_i

Expressing decomposition of a vector space V into direct sum of subspaces.

V = V_1 \sqcup V_2 \sqcup V_3

V = V_1 \sqcup V_2 \sqcup V_3