What is Set Theory? What are Sets?

“Set theory is the mathematical theory of well-determined collections, called sets, of objects that are called members, or elements, of the set.”1

A set is, to put it simply, a collection of unsorted objects, and as such, a set is defined by the objects it contains. The concept of sets is fundamental to the study of math and statistics, and it has numerous practical uses.2 For example: to represent, gather, and analyze comparable data, sets are frequently used.

Significance Of Sets

We frequently use math to help us think about issues that may not initially appear to be mathematical. One subject with surprisingly varied applications is set theory. Since every branch of math uses or refers to sets in some way, they are crucial in all areas of math. They are required for the creation of ever-more complex mathematical structures. Set theory also gets off to a very straightforward start; it only considers whether an object belongs or does not belong to a common set of objects that have been unambiguously described. Because they more formally encode the entirety of information of a particular type, sets are essential, and due to their focus on the invariance of sets, set theory is equally important.2

Examples of Sets in Real Life

Most of us have collections of our favorite things, groups of objects, like our favorite clothes, favorite foods, favorite people and places, etc. These are all parts of sets, and we use them every day. Here are a few examples of sets that are frequently used in our daily lives:2, 3

  1. Bookcase
Bookcase

One of the best examples of sets is a bookcase. You keep your books arranged in a specific way, either by alphabetical order, by genre, or by your personal favorites. As a result, groups of related books are stored separately from one another.

  1. Closet 
closet

You might also keep your clothes arranged in a manner where the dresses, trousers, pants, coats, shawls, socks, etc., are kept together as a set. These related clothing groups are separated and kept apart from other sets of clothing.

  1. Bags
bags

Bags can be excellent examples of sets regardless of the kind of bag you use, including lunch bags, school bags, and everyday bags. Most bags have specific sections where you can organize necessities in a way that is easily accessible. Your notepads, pens, pencils, textbooks, accessories, cash, snacks, etc., could be included in the examples of sets.

  1. Jewelry Box
Jewelry Box

Another common example that most people can relate to is a jewelry box. You may keep your jewelry in sorted sets, including rings, chains, necklaces, and earrings.

  1. Kitchen
Kitchen

Depending on our cooking preferences, we arrange our kitchen utensils and groceries in a particular way. Dishware like bowls, glasses, cups, and saucers are kept separate from plates, and pans and cutlery are kept in their own compartments. Sets of cooking utensils and other collections are kept apart in storage.

As seen above, there can be infinite examples of sets in our daily life. In addition to these, applications of set theory are frequently used in science and math fields like physics, biology, chemistry, as well as in electrical engineering and computer engineering. 

If you found this article on sets interesting, you can further explore the real-life examples of the golden ratio, linear functions, congruent triangles and triangles. Check out BYJU’s FutureSchool Blog for more interesting articles on math and its intriguing applications.

References:

  1. Set Theory (Stanford Encyclopedia of Philosophy). (n.d.). Retrieved August 25, 2022, from https://plato.stanford.edu/entries/set-theory/ 
  2. Mehta, A., & Student, V. Y. (2014). APPLICATIONS OF SETS. www.physicsforums.com 
  3. 7 Daily Life Examples Of Sets – StudiousGuy. (n.d.). Retrieved August 25, 2022, from https://studiousguy.com/daily-life-examples-of-sets/ 
Math, World of Math