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A set of polygons in an Euler diagram This set equals the one depicted above since both have the very same elements.. In mathematics, a set is a collection of different [1] things; [2] [3] [4] these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other ...
The number 9 is not in the intersection of the set of prime numbers {2, 3, 5, 7, 11 ... Intersection theory – Branch of algebraic geometry; List of set identities ...
The first several Bell numbers are B 0 = 1, B 1 = 1, B 2 = 2, B 3 = 5, B 4 = 15, B 5 = 52, and B 6 = 203 (sequence A000110 in the OEIS). Bell numbers satisfy the recursion + = = and have the exponential generating function
This article lists mathematical properties and laws of sets, involving the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations.
A set of six points (red), its six 2-sets (the sets of points contained in the blue ovals), and lines separating each -set from the remaining points (dashed black). In discrete geometry , a k {\displaystyle k} -set of a finite point set S {\displaystyle S} in the Euclidean plane is a subset of k {\displaystyle k} elements of S {\displaystyle S ...
If is a subset of a vector space then is said to be a symmetric set if it is symmetric with respect to the additive group structure of the vector space; that is, if =, which happens if and only if . The symmetric hull of a subset S {\displaystyle S} is the smallest symmetric set containing S , {\displaystyle S,} and it is equal to S ∪ − S ...
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