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Difference between revisions of "Empty set"

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The set which contains no elements. Notation: <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e035/e035590/e0355901.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e035/e035590/e0355902.png" />. In other words, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e035/e035590/e0355903.png" />. Moreover, any assertion that is always false could be used in this definition instead of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e035/e035590/e0355904.png" />. The empty set is a subset of any set.
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The set which contains no elements. Notation: $\emptyset$, $\Lambda$. In other words, $\{x:x\neq x\}$. Moreover, any assertion that is always false could be used in this definition instead of $x\neq x$. The empty set is a subset of any set.

Revision as of 12:43, 9 April 2014

The set which contains no elements. Notation: $\emptyset$, $\Lambda$. In other words, $\{x:x\neq x\}$. Moreover, any assertion that is always false could be used in this definition instead of $x\neq x$. The empty set is a subset of any set.

How to Cite This Entry:
Empty set. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Empty_set&oldid=31429
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article