A set in mathematics is a well-defined collection of distinct objects, called elements or members, considered as a single entity. These elements can be anything: numbers, symbols, points, variables, or even other sets. Sets are usually denoted by capital letters and their elements are listed inside curly braces, for example, A={1,2,3,4,5}A=\{1,2,3,4,5\}A={1,2,3,4,5}
. Key points about sets:
- Elements are distinct; repetition is not counted.
- The order of elements does not matter.
- Sets can be finite (with a limited number of elements) or infinite (like the set of all natural numbers).
- The empty set (or null set) has no elements and is denoted by ∅\emptyset ∅.
- Membership is expressed as x∈Ax\in Ax∈A if xxx is an element of set AAA, and x∉Ax\notin Ax∈/A if it is not.
- Sets can be described by listing elements (roster form) or by a property that defines the elements (set-builder form).
Sets form the foundation of modern mathematics and are studied in set theory, which provides rigorous definitions and operations on sets
