Empty Set


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Related to Empty Set: Infinite set

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 ?
2] + bx + c then the solution of (1) is the empty set [empty set], and the solution of (2) is {[x.
In B, the empty set is defined as follows: [empty set] [?
Such is the power of the empty set, the set with no elements.
Peano's construction of the set of natural numbers from an empty set gives us an illustration of the concept of creatio ex nihilo.
Unsurprisingly, the Axiom of the Empty Set asserts that just such a set exists.
In GET, the empty set ([empty set]) can be singleton subsets or multiple hypothesis sets.
The axioms of group G are the axioms of ZFC (formulae of the signature ([epsilon]>}), with exception of the axiom of empty set, which are relativized to the family S.
Vijay, who has recorded live sessions for Radio Two and played at Coventry's St Mary's Guildhall and the Godiva Festival, will share the stage with Men Diamler, the Empty Set and Parge.
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 more vocal of the students in the "zero camp" essentially argued that one simply lists out all the proper subsets of the given set, and observes that the empty set is one of these proper subsets.
In mathematics, the notation for the sound of one hand clapping is o, which means that the set of the empty set is one.
Many variables are involved in defensing the no-back empty set.