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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. The relationship of one set being a subset of another is called inclusion (or sometimes containment).
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.
In mathematics, especially measure theory, a set function is a function whose domain is a family of subsets of some given set and that (usually) takes its values in the extended real number line {}, which consists of the real numbers and .
Also, in probability, σ-algebras are pivotal in the definition of conditional expectation. In statistics, (sub) σ-algebras are needed for the formal mathematical definition of a sufficient statistic, [3] particularly when the statistic is a function or a random process and the notion of conditional density is not applicable.
The image of f is a subset of Y, shown as the yellow oval in the accompanying diagram. Any function can be restricted to a subset of its domain. The restriction of f : X → Y {\displaystyle f\colon X\to Y} to A {\displaystyle A} , where A ⊆ X {\displaystyle A\subseteq X} , is written as f | A : A → Y {\displaystyle \left.f\right|_{A}\colon ...
A three-dimensional plot of an indicator function, shown over a square two-dimensional domain (set X): the "raised" portion overlays those two-dimensional points which are members of the "indicated" subset (A). In mathematics, an indicator function or a characteristic function of a subset of a set is a function that maps elements of the subset ...
In group theory, a branch of mathematics, a subset of a group G is a subgroup of G if the members of that subset form a group with respect to the group operation in G. Formally, given a group G under a binary operation ∗, a subset H of G is called a subgroup of G if H also forms a group under the operation
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 ...