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  2. Subset - Wikipedia

    en.wikipedia.org/wiki/Subset

    Subset. 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.

  3. Power set - Wikipedia

    en.wikipedia.org/wiki/Power_set

    In mathematics, the power set (or powerset) of a set S is the set of all subsets of S, including the empty set and S itself. [1] In axiomatic set theory (as developed, for example, in the ZFC axioms), the existence of the power set of any set is postulated by the axiom of power set. [2] The powerset of S is variously denoted as P(S), 𝒫 (S ...

  4. Level set - Wikipedia

    en.wikipedia.org/wiki/Level_set

    When n = 3, a level set is called a level surface (or isosurface); so a level surface is the set of all real-valued roots of an equation in three variables x 1, x 2 and x 3. For higher values of n, the level set is a level hypersurface, the set of all real-valued roots of an equation in n > 3 variables. A level set is a special case of a fiber.

  5. List of set identities and relations - Wikipedia

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

    Three sets involved. [edit] In the left hand sides of the following identities, L{\displaystyle L}is the L eft most set, M{\displaystyle M}is the M iddle set, and R{\displaystyle R}is the R ight most set. Precedence rules. There is no universal agreement on the order of precedenceof the basic set operators.

  6. Set theory - Wikipedia

    en.wikipedia.org/wiki/Set_theory

    Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory — as a branch of mathematics — is mostly concerned with those that are relevant to mathematics as a whole. The modern study of set theory was ...

  7. Algebra of sets - Wikipedia

    en.wikipedia.org/wiki/Algebra_of_sets

    Fundamentals. 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".

  8. Union (set theory) - Wikipedia

    en.wikipedia.org/wiki/Union_(set_theory)

    In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection. [1] It is one of the fundamental operations through which sets can be combined and related to each other. A nullary union refers to a union of zero (⁠ ⁠) sets and it is by definition equal to the empty set.

  9. 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 ...

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