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  2. List of set identities and relations - Wikipedia

    en.wikipedia.org/wiki/List_of_set_identities_and...

    A left identity element that is also a right identity element if called an identity element. The empty set is an identity element of binary union and symmetric difference , and it is also a right identity element of set subtraction :

  3. Subset - Wikipedia

    en.wikipedia.org/wiki/Subset

    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 relationship of one set being a subset of another is called inclusion (or sometimes containment).

  4. Method of distinguished element - Wikipedia

    en.wikipedia.org/.../Method_of_distinguished_element

    The set of all size-k subsets contains: (1) all size-k subsets that do contain the distinguished element, and (2) all size-k subsets that do not contain the distinguished element. If a size-k subset of a size-(n + 1) set does contain the distinguished element, then its other k − 1 elements are chosen from among the other n elements of our ...

  5. Indicator function - Wikipedia

    en.wikipedia.org/wiki/Indicator_function

    In mathematics, an indicator function or a characteristic function of a subset of a set is a function that maps elements of the subset to one, and all other elements to zero. That is, if A is a subset of some set X, then () = if , and () = otherwise, where is a common notation for the indicator function.

  6. Algebra of sets - Wikipedia

    en.wikipedia.org/wiki/Algebra_of_sets

    The algebra of sets is the set-theoretic analogue of the algebra of numbers. Just as arithmetic addition and multiplication are associative and commutative, so are set union and intersection; just as the arithmetic relation "less than or equal" is reflexive, antisymmetric and transitive, so is the set relation of "subset".

  7. Set (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Set_(mathematics)

    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 ...

  8. Partition of a set - Wikipedia

    en.wikipedia.org/wiki/Partition_of_a_set

    A set of stamps partitioned into bundles: No stamp is in two bundles, no bundle is empty, and every stamp is in a bundle. The 52 partitions of a set with 5 elements. A colored region indicates a subset of X that forms a member of the enclosing partition. Uncolored dots indicate single-element subsets.

  9. Power set - Wikipedia

    en.wikipedia.org/wiki/Power_set

    The binomial theorem is closely related to the power set. 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 ...