In mathematics, a **finite set** is a set that has a finite number of elements. For example,

is a finite set with five elements. The number of elements of a finite set is a natural number (non-negative integer), and is called the cardinality of the set. A set that is not finite is called **infinite**. For example, the set of all positive integers is infinite:

Finite sets are particularly important in combinatorics, the mathematical study of counting. Many arguments involving finite sets rely on the pigeonhole principle, which states that there cannot exist an injective function from a larger finite set to a smaller finite set.

Read more about Finite Set: Definition and Terminology, Basic Properties, Necessary and Sufficient Conditions For Finiteness, Foundational Issues, Set-theoretic Definitions of Finiteness

### Famous quotes containing the words finite and/or set:

“For it is only the *finite* that has wrought and suffered; the infinite lies stretched in smiling repose.”

—Ralph Waldo Emerson (1803–1882)

“Life has been your art. You have *set* yourself to music. Your days are your sonnets.”

—Oscar Wilde (1854–1900)