Finite
In mathematics, a set is called finite if and only if there is a bijection between the set and some set of the form {1, 2, ..., n} where n is a natural number. All finite sets are countable, but not all countable sets are finite.
Related Topics:
Mathematics - Set - Bijection - Natural number - Countable
~ ~ ~ ~ ~ ~ ~ ~ ~ ~
It is a theorem (assuming the axiom of choice) that a set is finite if and only if there exists no bijection between the set and any of its proper subsets. Equivalently, a set is finite if its cardinality, i.e. the number of its elements, is a natural number. For instance, the set of integers between -15 and 3 is finite, since it has 17 elements. The set of all prime numbers is not finite. Sets that are not finite are called infinite.
Related Topics:
Theorem - Axiom of choice - Subset - Cardinality - Integer - Prime number - Infinite
~ ~ ~ ~ ~ ~ ~ ~ ~ ~
In physics, finite additionally means "non-zero", for instance in a sentence like "if the distance of the two objects is finite...".
~ ~ ~ ~ ~ ~ ~ ~ ~ ~
See also: infinity
~ ~ ~ ~ ~ ~ ~ ~ ~ ~
~ Table of Content ~
| ► | Introduction |
~ What's Hot ~
~ Community ~
| ► | History Forum Come and discuss about History, Civilizations, Historical Events and Figures |
| ► | History Web-Ring A community of sites, blogs and forums dedicated to History. Do not hesitate to submit your site. |
and are licensed under the GNU Free Documentation License.
Lexicon - Privacy Policy - Spiritus-Temporis.com ©2005.
