Set | Definition & Facts | Britannica (2024)

mathematics and logic

verifiedCite

While every effort has been made to follow citation style rules, there may be some discrepancies.Please refer to the appropriate style manual or other sources if you have any questions.

Select Citation Style

Feedback

Thank you for your feedback

Our editors will review what you’ve submitted and determine whether to revise the article.

Print

verifiedCite

While every effort has been made to follow citation style rules, there may be some discrepancies.Please refer to the appropriate style manual or other sources if you have any questions.

Select Citation Style

Feedback

Thank you for your feedback

Our editors will review what you’ve submitted and determine whether to revise the article.

Written and fact-checked by

The Editors of Encyclopaedia Britannica Encyclopaedia Britannica's editors oversee subject areas in which they have extensive knowledge, whether from years of experience gained by working on that content or via study for an advanced degree. They write new content and verify and edit content received from contributors.

The Editors of Encyclopaedia Britannica

Last Updated: Article History

Related Topics:
connectedness
universal set
ordered set
open set
null set

See all related content →

set, in mathematics and logic, any collection of objects (elements), which may be mathematical (e.g., numbers and functions) or not. A set is commonly represented as a list of all its members enclosed in braces. The intuitive idea of a set is probably even older than that of number. Members of a herd of animals, for example, could be matched with stones in a sack without members of either set actually being counted. The notion extends into the infinite. For example, the set of integers from 1 to 100 is finite, whereas the set of all integers is infinite. Because an infinite set cannot be listed, it is usually represented by a formula that generates its elements when applied to the elements of the set of counting numbers. Thus, {2x | x = 1, 2, 3,…} represents the set of positive even numbers (the vertical bar means “such that”).

To indicate that an object x is a member of a set A, one writes xA, while xA indicates that x is not a member of A. A set with no members is called an empty, or null, set and is denoted ∅. A set A is called a subset of a set B (symbolized by AB) if all the members of A are also members of B. For example, any set is a subset of itself, and Ø is a subset of any set. If both AB and BA, then A and B have exactly the same members. Part of the set concept is that in this case A = B; that is, A and B are the same set.

The symbol ∪ is employed to denote the union of two sets. Thus, the set AB—read “A union B” or “the union of A and B”—is defined as the set that consists of all elements belonging to either set A or set B or both. For example, if the set A is given by {1, 2, 3, 4, 5} and the set B is given by {1, 3, 5, 7, 9}, the set AB is {1, 2, 3, 4, 5, 7, 9}.

More From Britannicaset theory

The intersection operation is denoted by the symbol ∩. The set AB—read “A intersection B” or “the intersection of A and B”—is defined as the set composed of all elements that belong to both A and B. Thus, the intersection of the two sets in the previous example is the set {1, 3, 5}. For more information about sets and their use in mathematics, see set theory.

The Editors of Encyclopaedia BritannicaThis article was most recently revised and updated by Erik Gregersen.

Set | Definition & Facts | Britannica (2024)
Top Articles
Latest Posts
Recommended Articles
Article information

Author: Ray Christiansen

Last Updated:

Views: 6042

Rating: 4.9 / 5 (49 voted)

Reviews: 80% of readers found this page helpful

Author information

Name: Ray Christiansen

Birthday: 1998-05-04

Address: Apt. 814 34339 Sauer Islands, Hirtheville, GA 02446-8771

Phone: +337636892828

Job: Lead Hospitality Designer

Hobby: Urban exploration, Tai chi, Lockpicking, Fashion, Gunsmithing, Pottery, Geocaching

Introduction: My name is Ray Christiansen, I am a fair, good, cute, gentle, vast, glamorous, excited person who loves writing and wants to share my knowledge and understanding with you.