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:
“Put shortly, these are the two views, then. One, that man is intrinsically good, spoilt by circumstance; and the other that he is intrinsically limited, but disciplined by order and tradition to something fairly decent. To the one party man’s nature is like a well, to the other like a bucket. The view which regards him like a well, a reservoir full of possibilities, I call the romantic; the one which regards him as a very finite and fixed creature, I call the classical.”
—Thomas Ernest Hulme (1883–1917)
“There is one thing that matters—to set a chime of words tinkling in the minds of a few fastidious people.”
—Logan Pearsall Smith (1865–1946)