Set theory Developed at the end of the 19th century, set theory is now a ubiquitous part of mathematics. It can be used as a foundation from which nearly all of mathematics can be derived. In terms of English, a set is a group or collection of things that belong together or resemble one another or are usually found together. Say, for example, a set of pens, a set of storybooks, a set of toys and so on. In mathematics, a set is a well-defined collection of distinct objects, considered as an object in its own right. The arrangement of the objects in the set does not matter. A set may be denoted by placing its objects between a pair of curly braces. For example, the numbers 2, 4, and 6 are distinct objects when considered separately, but when they are considered collectively, they form a single set of size three, written {2,4,6}.