A set in mathematics is a collection of distinct objects. These objects can be anything: numbers, functions, other sets, and so on. The objects within a set are called elements or members of the set.

For example, `{1, 2, 3}`

is a set of numbers, and `{a, e, i, o, u}`

is a set of vowels in the English alphabet.

Sets are usually denoted by capital letters, while their elements are denoted by small letters. For instance, we might say “Let A be the set of all even numbers”.

The concept of sets is fundamental in mathematics and forms the basis of a branch called set theory, which is used as a foundational system for nearly all of mathematics.