Empty Set

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Related to Empty Set: Infinite set

empty set

[′em·tē ′set]
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 ?
Such is the power of the empty set, the set with no elements.
Put another way, the empty set is, in a sense--for Kuitca, for Lacan--the empty tomb.
Hence, a second way of signifying the empty set is to keep a secret, something passed down only from father to son.
It also has other coverages, linebacker stunts, and line games that are highly effective against empty sets.
Against the darkly painted wooden partition of the empty set, the models' light skin, plain underwear, and white stockings are brought into relief.
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.
Columns 3 and 4 show how these constructions act on two important special classes: the empty set ([empty set]) that does not contain any structure and the neutral class [epsilon] consisting of a single structure of size 0.
The gallery lighting was extremely low, the installation suffused with the theatricality of an empty set.
containers to empty sets and an anticoagulant fluid to collect plasma by plasmapheresis with an automatic plasma lease separators dedicated to the ordered sets1.
Running on empty sets you up for less effective training.
The empty sets force the defense to cover five good athletes.
One-dimensional acts like Korn, Sugar Ray, Blink 182 and Reel Big Fish offered energetic but ultimately empty sets.