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.
\mathbb{R} \Supset \mathbb{Z}Demonstrating that the set of complex numbers properly contains the real numbers.
\mathbb{C} \Supset \mathbb{R}Illustrating that the set of rational matrices is a proper superset of the set of integer matrices.
M_{n}(\mathbb{Q}) \Supset M_{n}(\mathbb{Z})