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:
“We know then the existence and nature of the finite, because we also are finite and have extension. We know the existence of the infinite and are ignorant of its nature, because it has extension like us, but not limits like us. But we know neither the existence nor the nature of God, because he has neither extension nor limits.”
—Blaise Pascal (1623–1662)
“Well, most men have bound their eyes with one or another handkerchief, and attached themselves to some of these communities of opinion. This conformity makes them not false in a few particulars, authors of a few lies, but false in all particulars. Their every truth is not quite true. Their two is not the real two, their four not the real four; so that every word they say chagrins us and we know not where to set them right.”
—Ralph Waldo Emerson (1803–1882)