Empty Set (original) (raw)
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The set containing no elements, commonly denoted 
or 
, the former of which is used in this work. These correspond to Wolfram Language and TeX characters summarized in the table below.
Unfortunately, some authors use the notation 0 instead of 
for the empty set (Mendelson 1997). The empty set is generally designated using 
(i.e., the empty list) in the Wolfram Language.
A set that is not the empty set is called a nonempty set. The empty set is sometimes also known as the null set (Mendelson 1997).
The complement of the empty set is the universal set.
Strangely, the empty set is both open and closed for any set 
and topology.
A groupoid, semigroup, quasigroup, ringoid, andsemiring can be empty. Monoids,groups, and rings must have at least one element, while division algebras andfields must have at least two elements.
See also
Nonempty Set, Set, Singleton Set, Trivial Topology, Universal Set, Urelement
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References
Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, p. 266, 1996.Mendelson, E. Introduction to Mathematical Logic, 4th ed. London: Chapman & Hall, 1997.
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Cite this as:
Weisstein, Eric W. "Empty Set." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/EmptySet.html