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cardinality is a unary operator. |
Arthur Rubin (talk | contribs) disputed; and move set difference to "derived binary operators" |
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* The '''empty set''' or '''null set''' is the set of no elements, denoted by <math>\varnothing</math> and sometimes 0.
* A '''unary operator''' applies to a single set. There are two{{disputed-inline}} unary operators. One is called logical '''NOT'''. It works by taking the [[complement (set theory)|complement]] with respect to the universe, i.e. the set of all elements under consideration. The other is the cardinality, which converts a set into a whole number, the number of elements.{{disputed-inline}} This is written as ''n(A)''.{{disputed-inline}}
* A '''binary operator''' applies to two sets. The basic binary operators are logical '''OR''' and logical '''AND'''. They perform the [[union (set theory)|union]] and [[intersection (set theory)|intersection]] of sets. The difference between sets, ''A-B'', is the set of all elements in ''A'' and not in ''B''.{{off-topic?}} The cartesian product, ''A×B'' is the set of ordered pairs taking one element from ''A'' and one from ''B''.{{disputed-inline}}
There are also other derived binary operators, such as '''XOR''' (exclusive OR, i.e., "one or the other, but not both"), and set difference, '''A-B'''.
* A '''subset''' is denoted by <math>A \subseteq B</math> and means every element in set A is also in set B.
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