# Empty Set

(redirected from*Non-empty set*)

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Related to Non-empty set: Proper subset

## empty set

[′em·tē ′set] (mathematics)

The set with no elements.

McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

The following article is from

*The Great Soviet Encyclopedia*(1979). It might be outdated or ideologically biased.## Empty Set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 *x ^{n}* +

*y*=

^{n}*z*, where

^{n}*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.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.