Set

A set is an object $A$ for which it makes sense to ask, for any object $x$, whether $x$ is an element of $A$, written $x \in A$.

In rigorous foundations (e.g., ZFC set theory), “set” and the membership relation $\in$ are taken as primitive notions satisfying axioms. In analysis, one typically uses sets to collect numbers, points, functions , or other mathematical objects into a single entity that can be quantified over. Key operations include union , intersection , and subset relations.

Examples:

• $\{1,2,3\}$ is the set whose elements are exactly the numbers $1,2,3$.
• $\mathbb{R}$ is the set of real numbers.
• $\varnothing$ is the set with no elements.