Definition:Subset/Superset

Definition

If $S$ is a subset of $T$, then $T$ is a superset of $S$.

This can be expressed by the notation $T \supseteq S$.

This can be interpreted as $T$ includes $S$, or (more rarely) $T$ contains $S$.

Thus $S \subseteq T$ and $T \supseteq S$ mean the same thing.

Also known as

The term superset is rare in the literature.

Instead of $T$ is a superset of $S$, the usual terminology is $T$ contains $S$ or $T$ includes $S$.

Also see

• Definition:Subset

Sources

• 1960: Paul R. Halmos: Naive Set Theory ... (previous) ... (next): $\S 1$: The Axiom of Extension
• 1963: George F. Simmons: Introduction to Topology and Modern Analysis ... (previous) ... (next): $\S 1$: Sets and Set Inclusion
• 1965: Claude Berge and A. Ghouila-Houri: Programming, Games and Transportation Networks ... (previous) ... (next): $1$. Preliminary ideas; sets, vector spaces: $1.1$. Sets
• 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text I$: Algebraic Structures: $\S 1$: The Language of Set Theory
• 1967: George McCarty: Topology: An Introduction with Application to Topological Groups ... (previous) ... (next): Introduction: Set-Theoretic Notation
• 1971: Robert H. Kasriel: Undergraduate Topology ... (previous) ... (next): $\S 1.3$: Subsets
• 1979: John E. Hopcroft and Jeffrey D. Ullman: Introduction to Automata Theory, Languages, and Computation ... (previous) ... (next): Chapter $1$: Preliminaries: $1.4$ Set Notation
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics: Superset