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Set - Cardinality of a set | | Set - Cardinality of a set: Encyclopedia II - Set - Cardinality of a set | | Each of the sets described above has a definite number of members; for example, the set A has four members, while the set B has three members.
A set can also have zero members. Such a set is called the empty set (or the null set) and is denoted by the symbol ø. For example, the set A of all three-sided squares has zero members, and thus A = ø. Like the number zero, though seemingly trivial, the empty set turns out to be quite important in mathematics.
For more information on the empty set see Empty set.
A set can also have an infinite number of members; for exam ...
See also:Set, Set - Definition, Set - Describing sets, Set - Descriptions using words or lists, Set - Descriptions using mathematical notation, Set - Set membership, Set - Cardinality of a set, Set - Subsets, Set - Special sets, Set - Unions, Set - Intersections, Set - Complements | | | Set, Set - Cardinality of a set, Set - Complements, Set - Definition, Set - Describing sets, Set - Descriptions using mathematical notation, Set - Descriptions using words or lists, Set - Intersections, Set - Set membership, Set - Special sets, Set - Subsets, Set - Unions, Alternative set theory, Class (set theory), Family (mathematics), Mathematical structure, Multiset, Tuple | | |
| | | Set: Encyclopedia II - Set - Cardinality of a set
Set - Cardinality of a set
Each of the sets described above has a definite number of members; for example, the set A has four members, while the set B has three members.
A set can also have zero members. Such a set is called the empty set (or the null set) and is denoted by the symbol ø. For example, the set A of all three-sided squares has zero members, and thus A = ø. Like the number zero, though seemingly trivial, the empty set turns out to be quite important in mathematics.
For more information on the empty set see Empty set.
A set can also have an infinite number of members; for example, the set of natural numbers is infinite.
For more information on infinity and the size of sets, see cardinality and cardinal number.
For more information on finite sets and counting them, see combinatorics and permutations and combinations.
Other related archives19th century, Alternative set theory, Class (set theory), Complement (set theory), Empty set, Family (mathematics), French flag, Intersection (set theory), Mathematical structure, Multiset, Set theory, Set-builder notation, Subset, Tuple, Union (set theory), axiomatic, axiomatic set theory, braces, cardinal number, cardinality, collection, combinatorics, complex numbers, concepts, elements, ellipsis, equality, expression, improper fractions, infinity, integers, intuitive, irrational, mathematics, mathematics education, multiset, naive set theory, natural numbers, permutations and combinations, powers of two, primary school, proper, rational numbers, real numbers, relationship, set theory, theory, universal set, whole, whole numbers
 Adapted from the Wikipedia article "Cardinality of a set", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki |
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