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  2. Universal set - Wikipedia

    en.wikipedia.org/wiki/Universal_set

    In set theory, a universal set is a set which contains all objects, including itself. [1] In set theory as usually formulated, it can be proven in multiple ways that a universal set does not exist. However, some non-standard variants of set theory include a universal set.

  3. 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 ...

  4. Xi (letter) - Wikipedia

    en.wikipedia.org/wiki/Xi_(letter)

    A universal set in set theory; ... The following characters are used only as mathematical symbols. Stylized Greek text should be encoded using the normal Greek ...

  5. 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 ...

  6. Naive set theory - Wikipedia

    en.wikipedia.org/wiki/Naive_set_theory

    For instance, when investigating properties of the real numbers R (and subsets of R), R may be taken as the universal set. A true universal set is not included in standard set theory (see Paradoxes below), but is included in some non-standard set theories. Given a universal set U and a subset A of U, the complement of A (in U) is defined as

  7. 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.

  8. Intersection (set theory) - Wikipedia

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

    So the intersection of the empty family should be the universal set (the identity element for the operation of intersection), [4] but in standard set theory, the universal set does not exist. However, when restricted to the context of subsets of a given fixed set X {\displaystyle X} , the notion of the intersection of an empty collection of ...

  9. 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.