 |
|
| |
|
|
|
at Global Oneness Community.
Share your dreams and let others help you with the interpretation!
Dream Sharing Forum
|
|
Set - Complements | | Set - Complements: Encyclopedia II - Set - Complements | | Two sets can also be "subtracted". The relative complement of A in B (also called the set theoretic difference of B and A), denoted by B − A, (or B \ A) is the set of all elements which are members of B, but not members of A. Note that it is valid to "subtract" members of a set that are not in the set, such as removing green fr ...
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 - Complements
Set - Complements
Two sets can also be "subtracted". The relative complement of A in B (also called the set theoretic difference of B and A), denoted by B − A, (or B \ A) is the set of all elements which are members of B, but not members of A. Note that it is valid to "subtract" members of a set that are not in the set, such as removing green from {1,2,3}; doing so has no effect.
In certain settings all sets under discussion are considered to be subsets of a given universal set U. In such cases, U − A, is called the absolute complement or simply complement of A, and is denoted by A′.
Examples:
- {1, 2} − {red, white} = {1, 2}
- {1, 2, green} − {red, white, green} = {1, 2}
- {1, 2} − {1, 2} = ø
- If U is the set of integers, E is the set of even integers, and O is the set of odd integers, then the complement of E in U is O, or equivalently, E′ = O.
Some basic properties of complements:
- A U A′ = U
- A ∩ A′ = ø
- (A′ )′ = A
- A − A = ø
- A − B = A ∩ B′
For more information about complements of sets, see Complement (set theory).
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 "Complements", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki |
|
|
|
More material related to Set can be found here:
|
|
|
« Back
|
Search the Global Oneness web site |
|
|
|
|
|
Sneak-Peek of Global Oneness Community
Hi friend! The Global Oneness Community, the place for information and sharing about Oneness is not really launched yet (you will see there is still some clean up to do) ...but it is now open for a sneak-peek! And if you wish - please register and become one of the very first members to do so! Jonas
Forum Home,
Articles,
Photo Gallery,
Videos,
News,
Sitemap
...and much more!
|
