Empty Set -- From Wolfram MathWorld

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The set containing no elements, commonly denoted emptyset or emptyset, the former of which is used in this work. These correspond to Wolfram Language and TeX characters summarized in the table below.

symbolTeXWolfram Language
emptyset\varnothing\[Diameter]
emptyset\emptyset\[EmptySet]

Unfortunately, some authors use the notation 0 instead of emptyset 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 X and topology.

A groupoid, semigroup, quasigroup, ringoid, and semiring can be empty. Monoids, groups, and rings must have at least one element, while division algebras and fields 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.

Referenced on Wolfram|Alpha

Empty Set

Cite this as:

Weisstein, Eric W. "Empty Set." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/EmptySet.html

Subject classifications

  • Foundations of Mathematics
  • Set Theory
  • Sets
Created, developed and nurtured by Eric Weisstein at Wolfram Research

Tag » What Is The Empty Set