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A is a subset of B (denoted ) and, conversely, B is a superset of A (denoted ). In mathematics, a set A is a subset of a set B if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be equal; if they are unequal, then A is a proper subset of B.
The subset sum problem (SSP) is a decision problem in computer science. In its most general formulation, there is a multiset of integers and a target-sum , and the question is to decide whether any subset of the integers sum to precisely . [1] The problem is known to be NP-complete.
In linear algebra, the closure of a non-empty subset of a vector space (under vector-space operations, that is, addition and scalar multiplication) is the linear span of this subset. It is a vector space by the preceding general result, and it can be proved easily that is the set of linear combinations of elements of the subset.
The only subset of the empty set is the empty set itself; equivalently, the power set of the empty set is the set containing only the empty set. The number of elements of the empty set (i.e., its cardinality) is zero. The empty set is the only set with either of these properties. For any set A: The empty set is a subset of A
In this poset, 60 is an upper bound (though not a least upper bound) of the subset {,,,}, which does not have any lower bound (since 1 is not in the poset); on the other hand 2 is a lower bound of the subset of powers of 2, which does not have any upper bound. If the number 0 is included, this will be the greatest element, since this is a ...
A nested set collection or nested set family is a collection of sets that consists of chains of subsets forming a hierarchical structure, like Russian dolls. It is used as reference concept in scientific hierarchy definitions, and many technical approaches, like the tree in computational data structures or nested set model of relational databases.
In mathematics, a multiset (or bag, or mset) is a modification of the concept of a set that, unlike a set, [1] allows for multiple instances for each of its elements.The number of instances given for each element is called the multiplicity of that element in the multiset.
A k –elements combination from some set is another name for a k –elements subset, so the number of combinations, denoted as C(n, k) (also called binomial coefficient) is a number of subsets with k elements in a set with n elements; in other words it's the number of sets with k elements which are elements of the power set of a set with n ...