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 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].
Then a L-fuzzy subset A of a non-empty set X is defined as a function A : X [right arrow] L.
An Intuitionistic Fuzzy Subset (IFS) A in a non-empty set X is defined as an object of the form A = {< x, [[mu].
3] A SU-algebra is a non-empty set X with a constant 0 and a binary operation "*" satisfying the following axioms:
22] A PM-space is an ordered pair (X, F), where X is a non-empty set and F is a mapping from X x X to [?
14] Let A and S be two self mappings of non-empty set X x A point x [member of] X is called a coincidence point of A and S if and only if Ax = Sx.
12] Two self mappings A and S of a non-empty set X are said to be weakly compatible if they commute at their coincidence points, that is, if Ax = Sx for some x [member of] X, then ASx = SAx.
By an algebra G = (G, *, 0) we mean a non-empty set G together with a binary operation, multiplication and a some distinguished element 0.
is a non-empty set, where E is the set of all idempotents of S.
Definition [1]: A groupoid (G, *) is a non-empty set, closed with respect to an operation * (in general * need not to be associative).