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Difference between revisions of "Empty 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 statement $x \in \emptyset$ is always false.  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.   
  
 
====References====
 
====References====
 
<table>
 
<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>
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<TR><TD valign="top">[a1]</TD> <TD valign="top"> P. R. Halmos, ''Naive Set Theory'', Springer (1960) {{ISBN|0-387-90092-6}}</TD></TR>
 
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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=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