Empty Set

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Related to Non-empty: 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 ?
2] are disjoint non-empty compact subsets, one has [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
If we assume that each non-empty container thus only has one bean, we're left with the conclusion that the sack contained exactly 100 jelly beans.
J](A) [intersection] (X - U) is a non-empty J-closed subset of [c.
beta]GO-connected) if X can not be written as a disjoint union of two non-empty [theta]-[beta]g-open (resp.
Let f be a locally bounded measurable function, which is continuous on [partial derivative]X and let B and W be two non-empty finite subsets of a lattice L.
A non-empty subset S of a BF-algebra X is said to be a subalgebra if
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j] if, for every [alpha] [member of] [DELTA], there exists a non-empty ([[tau].
is a function assigning a non-empty collection U(x) to each x [member of] X, of parts of X satisfying i), ii), iii), then the collection T of those sets U such that U [member of] U(x) for each x of U is a topology of X.
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