Empty Set

(redirected from Non-empty set)
Also found in: Dictionary.
Related to Non-empty set: 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 ?
Let B be a non-empty set and L(a) be a system of complete lattices.
Let X ba a non-empty set and [lambda] be the generalized topology on X and A [subset or equal to] X.
Separating these edges, we obtain a non-empty set of hollow hypertrees with edges decorated by [?
A fuzzy subset [mu] in a non-empty set X is a function [mu]: X [right arrow] [0,1].
An assignment is said to satisfy a diagram D if and only if it satisfies all the representing facts of D, where an assignment satisfies the representing facts if, basically, any shaded region is assigned the empty set and any region with an x-sequence in it is assigned a non-empty set.
Definition 3 [20] Let X is a non-empty set, and the NCSs A and B in the form A = {[A.
In 1965, Zadeh defined fuzzy subset of a non-empty set as a collection of objects with grade of membership in continum, with each object being assigned a value between 0 and 1 by a membership function [1].
Let X be a non-empty set and P(X) be the power set of X .
1 [7] Let X be any non-empty set and B [subset or equal to] F (X) be a binary domain.
An intuitionistic fuzzy set A in a non-empty set X is an object having the form A = {(x,[[mu].
3] An intuitionistic Fuzzy topology (IFT) in Coker's sense on a non-empty set X is a family [tau] of IFSs in X satisfying the following axioms.
c) A closed up interval is a non-empty set S [subset or equal to] [U.