Empty Set

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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 ?
of non empty partitions and the "Mobius-like" arithmetical function, [upsilon], defined on the set, [N.
1] is a non empty vg- open set in X such that vg[bar.
0]-limit point of X, we can choose a non empty vg-open [V.
1A restricted interval valued neutrosophic topology (RIVN-topology in short) on a non empty set X is a family of restricted interval valued neutrosophic subsets in X satisfying the following axioms
is the empirical distribution of m urns when, starting with distribution w, one ball is removed from every non empty urn and then balls are thrown at random until [rm] urns are non empty again, balls overflowing the capacity C being rejected.
n] defined by (1) of successive batches are thrown in urns until [rm] urns are non empty.
5] 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.
Let X = {a,b} be a non empty set, A = [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
A non empty set X together with two topologies [[tau].
ii) iff Every class of ) semi closed sets with finite intersection property has non empty intersection.
ii) iff Every class of pairwise closed sets with finite intersection property has non empty intersection.

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