Empty Set

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Related to Non-empty subset: Proper subset

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 ?
3] A non-empty subset I of a BT-algebra X is said to be an ideal of X if
if every non-empty subset contains finitely many minimal elements(this number being non-zero).
c] induced by the Coxeter element c and a non-empty subset I [subset or equal to] [n].
A non-empty subset A of a binary algebra X is called an ideal of X if it satisfies the following conditions:
A non-empty subset S of X is called a subalgebra of X if x * y [member of] S whenever x,y [member of] S.
12] In an arbitrary strictly i-coloring of H, the vertex's set X of H'certainly is divided into i partition, each partition is a non-empty subset of monochrome, we call it as the color category.
Let X be a real Banach space, and K a non-empty subset of X, T a self mapping of K and F(T), D(T) and I are the set of fixed points, domain of T and identity operator respectively.
Then a non-empty subset S of G is said to be a KU-subalgebra of G if(S, *, 0) is KU-algebra.
Let D, E are two ideals of H such that D [subset or equal to] E and let A be a non-empty subset of H.
Consider a directed tree S whose vertices are labeled by non-empty subsets of V.
t] of [n] into pairwise disjoint non-empty subsets, we say that S is a non-crossing partition if any two parts Si and Sj are non-crossing.
If S is regarded as a regular set and dividing the rest of n-1 elements into three non-empty subsets, the number of partitions is [S.

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