TeXipedia

Supset

Represents a strict superset relationship where one set properly contains all elements of another set, with an additional line beneath for emphasis.

Overview

Serves as a specialized mathematical notation in set theory and related fields to indicate a proper superset relationship with added emphasis through an underline.

  • Commonly used in advanced mathematics and theoretical computer science when precise set relationships need to be distinguished.
  • Particularly useful when multiple levels of set containment need to be clearly differentiated.
  • Often appears alongside other set theory symbols in formal proofs and mathematical logic.
  • Provides a more visually distinct alternative to the standard superset symbol when emphasis is needed.

Examples

Showing that the set of real numbers is a proper superset of the integers.

RZ\mathbb{R} \Supset \mathbb{Z}
\mathbb{R} \Supset \mathbb{Z}

Demonstrating that the set of complex numbers properly contains the real numbers.

CR\mathbb{C} \Supset \mathbb{R}
\mathbb{C} \Supset \mathbb{R}

Illustrating that the set of rational matrices is a proper superset of the set of integer matrices.

Mn(Q)Mn(Z)M_{n}(\mathbb{Q}) \Supset M_{n}(\mathbb{Z})
M_{n}(\mathbb{Q}) \Supset M_{n}(\mathbb{Z})