Difference between revisions of "Empty set"
From Encyclopedia of Mathematics
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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. | + | 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 statement $x \in \emptyset$ is always false. The empty set is a subset of any set. |
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| + | ====References==== | ||
| + | <table> | ||
| + | <TR><TD valign="top">[a1]</TD> <TD valign="top"> P. R. Halmos, ''Naive Set Theory'', Springer (1960) ISBN 0-387-90092-6</TD></TR> | ||
| + | </table> | ||
Revision as of 20:39, 5 December 2014
2020 Mathematics Subject Classification: Primary: 03E [MSN][ZBL] 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 statement $x \in \emptyset$ is always false. The empty set is a subset of any set.
References
| [a1] | P. R. Halmos, Naive Set Theory, Springer (1960) ISBN 0-387-90092-6 |
How to Cite This Entry:
Empty set. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Empty_set&oldid=35371
Empty set. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Empty_set&oldid=35371
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article