supseteq

Denotes a superset-or-equal relationship between sets, indicating that one set contains all elements of another set.

Overview

Essential in set theory and mathematical logic for expressing containment relationships between sets where equality is possible. Common applications include:

Proving set relationships in abstract algebra
Expressing subset hierarchies in computer science
Demonstrating containment properties in topology
Formalizing mathematical proofs where set inclusion needs to be shown

Often used alongside its counterpart subseteq to establish bidirectional set relationships or prove set equality.

Examples

Showing that set A contains set B as a subset.

A \supseteq B

A \supseteq B

Expressing that the real numbers contain the integers.

\mathbb{R} \supseteq \mathbb{Z}

\mathbb{R} \supseteq \mathbb{Z}

Demonstrating a sequence of nested set relationships.

X \supseteq Y \supseteq Z

X \supseteq Y \supseteq Z