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  2. 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 ...

  3. Element (mathematics) - Wikipedia

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

    In mathematics, an element (or member) of a set is any one of the distinct objects that belong to that set. For example, given a set called A containing the first four positive integers (= {,,,}), one could say that "3 is an element of A", expressed notationally as .

  4. List of set identities and relations - Wikipedia

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

    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.

  5. List of types of sets - Wikipedia

    en.wikipedia.org/wiki/List_of_types_of_sets

    List of set identities and relations – Equalities for combinations of sets; List of types of functions This page was last edited on 20 April 2024, at 21:36 ...

  6. Union (set theory) - Wikipedia

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

    If M is a set or class whose elements are sets, then x is an element of the union of M if and only if there is at least one element A of M such that x is an element of A. [11] In symbols: x ∈ ⋃ M ∃ A ∈ M , x ∈ A . {\displaystyle x\in \bigcup \mathbf {M} \iff \exists A\in \mathbf {M} ,\ x\in A.}

  7. Glossary of mathematical symbols - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_mathematical...

    A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols are needed for ...

  8. Glossary of set theory - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_set_theory

    1. The difference of two sets: x~y is the set of elements of x not in y. 2. An equivalence relation \ The difference of two sets: x\y is the set of elements of x not in y. − The difference of two sets: x−y is the set of elements of x not in y. ≈ Has the same cardinality as × A product of sets / A quotient of a set by an equivalence ...

  9. Intersection (set theory) - Wikipedia

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

    If is a nonempty set whose elements are themselves sets, then is an element of the intersection of if and only if for every element of , is an element of . In symbols: ( x ∈ ⋂ A ∈ M A ) ⇔ ( ∀ A ∈ M , x ∈ A ) . {\displaystyle \left(x\in \bigcap _{A\in M}A\right)\Leftrightarrow \left(\forall A\in M,\ x\in A\right).}