# Set Theory - Definitions, Properties, Operations, Applications Of Set Theory

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sets fields developing generality

Set theory is concerned with understanding those properties of sets that are independent of the particular elements that make up the sets. Thus the axioms and theorems of set theory apply to all sets in general, whether they are composed of numbers or physical objects. The foundations of set theory were largely developed by the German mathematician George Cantor in the latter part of the nineteenth century. The generality of set theory leads to few direct practical applications. Instead, precisely because of its generality, portions of the theory are used in developing the **algebra** of groups, rings, and fields, as well as, in developing a logical basis for **calculus**, **geometry**, and **topology**. These branches of **mathematics** are all applied extensively in the fields of **physics**, **chemistry**, **biology**, and electrical and computer **engineering**.

## Additional Topics

A set is a collection. As with any collection, a set is composed of objects, called members or elements. The elements of a set may be physical objects or mathematical objects. A set may be composed of baseball cards, salt shakers, tropical fish, numbers, geometric shapes, or abstract mathematical constructs such as functions. Even ideas may be elements of a set. In fact, the elements of a set are …

Two sets S and T are equal, if every element of the set S is also an element of the set T, and if every element
Figure 1a. Illustration by Hans & Cassidy. Courtesy of Gale Group.
Figure 2a. Illustration by Hans & Cassidy. Courtesy of Gale Group.
Figure 2c. Illustration by Hans & Cassidy. Courtesy of Gale Group.
of the set T is also an element of the set…

Because of its very general or abstract nature, set theory has many applications in other branches of mathematics. In the branch called analysis, of which differential and integral calculus are important parts, an understanding of limit points and what is meant by the continuity of a function are based on set theory. The algebraic treatment of set operations leads to boolean algebra, in which the …

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## User Comments

over 7 years ago

jacob Vernon

Set Theory - Definitions, Properties, Operations, Applications Of Set Theory

over 4 years ago

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over 4 years ago

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over 3 years ago

tareki

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about 2 years ago

the collection of well define element as called the set