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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 ...
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.
A Voronoi diagram is a special kind of decomposition of a metric space determined by distances to a specified discrete set of objects in the space, e.g., by a discrete set of points. This diagram is named after Georgy Voronoi , also called a Voronoi tessellation , a Voronoi decomposition, or a Dirichlet tessellation after Peter Gustav Lejeune ...
A Venn diagram, also called a set diagram or logic diagram, shows all possible logical relations between a finite collection of different sets. These diagrams depict elements as points in the plane, and sets as regions inside closed curves. A Venn diagram consists of multiple overlapping closed curves, usually circles, each representing a set.
The following table lists many specialized symbols commonly used in modern mathematics, ordered by their introduction date. The table can also be ordered alphabetically by clicking on the relevant header title.
That is, if A is a subset of some set X, then if , and otherwise, where is one common notation for the indicator function; other common notations are , , [a] and ( ) . The indicator function of A is the Iverson bracket of the property of belonging to A ; that is,
Rather, there are only three elements of B, namely the numbers 1 and 2, and the set {,}. The elements of a set can be anything. For example the elements of the set = {,,} are the color red, the number 12, and the set B.
In mathematics, a structure on a set (or on some sets) refers to providing it (or them) with certain additional features (e.g. an operation, relation, metric, or topology). Τhe additional features are attached or related to the set (or to the sets), so as to provide it (or them) with some additional meaning or significance.
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