Difference between revisions of "Empty set"
From Encyclopedia of Mathematics
(Importing text file) |
m (→References: isbn link) |
||
| (3 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
| − | The set which contains no elements. Notation: | + | {{TEX|done}}{{MSC|03E}} |
| + | |||
| + | 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==== | ||
| + | <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> | ||
Latest revision as of 08:09, 18 November 2023
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=16423
Empty set. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Empty_set&oldid=16423
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article