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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 common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the subsequent columns contains an informal explanation, a short example, the Unicode location, the name for use in HTML documents, [1] and the LaTeX symbol.
However, the definition of maximal and minimal elements is more general. In particular, a set can have many maximal and minimal elements, whereas infima and suprema are unique. Whereas maxima and minima must be members of the subset that is under consideration, the infimum and supremum of a subset need not be members of that subset themselves.
The first shown partition contains five single-element subsets; the last partition contains one subset having five elements. The traditional Japanese symbols for the 54 chapters of the Tale of Genji are based on the 52 ways of partitioning five elements (the two red symbols represent the same partition, and the green symbol is added for ...
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 ...
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
The expressions "A includes x" and "A contains x" are also used to mean set membership, although some authors use them to mean instead "x is a subset of A". [2] Logician George Boolos strongly urged that "contains" be used for membership only, and "includes" for the subset relation only. [3] For the relation ∈ , the converse relation ∈ T ...
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 ...