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Set - Subsets | | Set - Subsets: Encyclopedia II - Set - Subsets | | If every member of the set A is also a member of the set B, then A is said to be a subset of B, written , also pronounced A is contained in B. Equivalently, we can write , read as B is a superset of A, B includes A, or B contains A. The relationship between sets established by is called inclusion or containment.
If A is a subset of but not equal to B, then A is called a proper subset of B, written (A is a proper subset ...
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 - Subsets
Set - Subsets
If every member of the set A is also a member of the set B, then A is said to be a subset of B, written , also pronounced A is contained in B. Equivalently, we can write , read as B is a superset of A, B includes A, or B contains A. The relationship between sets established by is called inclusion or containment.
If A is a subset of but not equal to B, then A is called a proper subset of B, written (A is a proper subset of B) or (B is proper superset of A). However, in some literature these symbols are read the same as and , so it's often preferred to use the more explicit symbols and for proper subsets and supersets.
Examples:
- The set of all men is a proper subset of the set of all people.
The empty set is a subset of every set and every set is a subset of itself:
For more information about subsets, see Subset.
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 "Subsets", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki |
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