# Empty Set

(redirected from Nonempty)
Also found in: Dictionary, Wikipedia.
Related to Nonempty: Proper subset

## empty set

[′em·tē ′set]
(mathematics)
The set with no elements.

## Empty Set

(or null set), the set that contains no elements. The concept of the empty set, like the concept of zero, arises from the need to have the result of any operation on sets also be a set. The source of the concept of the empty set is the very method of defining a set by a characteristic property of its elements, since it may not be known beforehand whether elements possessing the property do in fact exist. Thus, it still is not known whether the equation xn + yn = zn, where n is an integer greater than 2, can be solved for x, y, and z if x, y, and z are natural numbers. In other words, it still is not known whether the set of those n > 2 for which the equation is solvable is empty or nonempty.

References in periodicals archive ?
9] A neutrosophic topology (NT) on a nonempty set X is a family T of neutrosophic sets in X satisfying the following axioms:
n]) [right arrow] 0 as n [right arrow] [infinity], then [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is nonempty and compact.
A]) is a nonempty, closed, bounded, convex, P- decomposable and weakly compact subset of [L.
Specially, the projection operator on a nonempty closed convex set V [subset or equal to] [R.
Partial array A of size (m, n) over [SIGMA], a nonempty set or an alphabet, is partial function A: [Z.
Let M be a nonempty subset of a Hausdorff topological vector space X and let F : M [right arrow] [2.
While the above problem seems hard, it is easy to prove that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is nonempty for all n [greater than or equal to] 2.
1: [8]A fuzzy finite state machine is a triple M = (Q x X x Q),where Q and X are finite nonempty sets and p is a membership of some fuzzy subsets of Q x X x Q, i.
L])] is nonempty and an equilibrium with unused observables that is profit maximizing for incumbents [I.
Nygaard and Werner [10] showed that in every infinite-dimensional uniform algebra, every nonempty relatively weakly open subset of its closed unit ball has diameter 2.
It is not compatible with a world in which there is no H or M, because it asserts that 1) both the set of humans and the set of mortals are nonempty, and 2) their intersection too is non-empty, i.
U, called universe of discourse, is a finite nonempty set for objects;

Site: Follow: Share:
Open / Close