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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. Set-builder notation - Wikipedia

    en.wikipedia.org/wiki/Set-builder_notation

    Set-builder notation can be used to describe a set that is defined by a predicate, that is, a logical formula that evaluates to true for an element of the set, and false otherwise. [2] In this form, set-builder notation has three parts: a variable, a colon or vertical bar separator, and a predicate. Thus there is a variable on the left of the ...

  4. Euler diagram - Wikipedia

    en.wikipedia.org/wiki/Euler_diagram

    Euler diagram illustrating that the set of "animals with four legs" is a subset of "animals", but the set of "minerals" is a disjoint set (it has no members in common) with "animals" Euler diagram showing the relationships between different Solar System objects

  5. Venn diagram - Wikipedia

    en.wikipedia.org/wiki/Venn_diagram

    A Venn diagram is a widely used diagram style that shows the logical relation between sets, popularized by John Venn (1834–1923) in the 1880s. The diagrams are used to teach elementary set theory, and to illustrate simple set relationships in probability, logic, statistics, linguistics and computer science.

  6. Category of sets - Wikipedia

    en.wikipedia.org/wiki/Category_of_sets

    Every set is a projective object in Set (assuming the axiom of choice). The finitely presentable objects in Set are the finite sets. Since every set is a direct limit of its finite subsets, the category Set is a locally finitely presentable category. If C is an arbitrary category, the contravariant functors from C to Set are often an important ...

  7. Set theory - Wikipedia

    en.wikipedia.org/wiki/Set_theory

    Set theory begins with a fundamental binary relation between an object o and a set A. If o is a member (or element) of A, the notation o ∈ A is used. A set is described by listing elements separated by commas, or by a characterizing property of its elements, within braces { }. [5]

  8. 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".

  9. Closed set - Wikipedia

    en.wikipedia.org/wiki/Closed_set

    A closed set contains its own boundary. In other words, if you are "outside" a closed set, you may move a small amount in any direction and still stay outside the set. This is also true if the boundary is the empty set, e.g. in the metric space of rational numbers, for the set of numbers of which the square is less than

  1. Related searches methods of describing a set

    two methods of describing a set