A set is any collection of elements. Sets can be related to each other in various ways; one important way sets can be related is that one set could be a subset of another. One set, $$A$$, is a subset of another, $$B$$, if and only if all elements of $$A$$ are elements of $$B$$. This is denoted $$A \subseteq B$$. Notably, $$A$$ can be a subset of $$B$$ even if there are no elements in $$B$$ that are not also in $$A$$ (i.e., they contain exactly the same elements). When $$B$$ contains additional elements that are not in $$A$$, $$A$$ is called a "proper subset" of $$B$$. This is denoted $$A \subset B$$. The same relationship between these sets can be indicated by calling $$B$$ a "superset", or "proper superset", of $$A$$ ($$B \supseteq A$$, or $$B \supset A$$, respectively), but referring to the [potentially] smaller set as a subset is more common.