subset

Denotes a proper subset relationship where one set is completely contained within another set, with the two sets not being equal.

Overview

Essential in set theory and mathematical logic for expressing hierarchical relationships between sets. Particularly common in:

Pure mathematics for defining set relationships
Computer science when describing data structures and algorithms
Logic proofs and formal mathematical writing
Database theory for expressing relationships between data sets

Often used alongside other set notation symbols to build complex mathematical statements about set relationships and hierarchies. The strict subset relationship it represents is fundamental to understanding set theory fundamentals and proving mathematical theorems.

Examples

Showing that set A is a proper subset of set B.

A \subset B

A \subset B

Expressing that the real numbers are a subset of the complex numbers.

\mathbb{R} \subset \mathbb{C}

\mathbb{R} \subset \mathbb{C}

Demonstrating nested subsets in number systems.

\mathbb{N} \subset \mathbb{Z} \subset \mathbb{Q} \subset \mathbb{R}

\mathbb{N} \subset \mathbb{Z} \subset \mathbb{Q} \subset \mathbb{R}