Finite Sets: Definition, Cardinality, And Examples In Mathematics

finite set

a set with a countable number of elements ( has an ending point)

A finite set is a set that contains a specific, finite number of elements. In other words, a finite set is a set that can be counted and the countable number of a finite set is called its cardinality. For example, let’s consider the set {1,2,3}. This set contains three elements and is therefore a finite set. Another example of a finite set is the set of months in a year, {January, February, March, April, May, June, July, August, September, October, November, December}, which contains twelve elements.

The notion of a finite set is often contrasted with an infinite set, which contains an unlimited number of elements. The concept of finite sets is used in various areas of mathematics, including algebra, set theory, and combinatorics, among others. A finite set can be represented using roster notation, which involves listing its elements within braces. For example, the set of even numbers less than 10 can be represented as {2, 4, 6, 8}.

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