Empty Set
المؤلف:
Conway, J. H. and Guy, R. K
المصدر:
The Book of Numbers. New York: Springer-Verlag
الجزء والصفحة:
...
13-1-2022
2121
Empty Set
The set containing no elements, commonly denoted 
or 
, the former of which is used in this work. These correspond to Wolfram Language and TeX characters summarized in the table below.
| symbol |
TeX |
Wolfram Language |
 |
varnothing |
[Diameter] |
 |
emptyset |
[EmptySet] |
Unfortunately, some authors use the notation 0 instead of 
for the empty set (Mendelson 1997). The empty set is generally designated using ![<span style=]()
{" src="https://mathworld.wolfram.com/images/equations/EmptySet/Inline6.svg" style="height:22px; width:6px" />![<span style=]()
}" src="https://mathworld.wolfram.com/images/equations/EmptySet/Inline7.svg" style="height:22px; width:6px" /> (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 
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.
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.
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