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35 relations: Array data type, Cartesian product, Category theory, Coproduct, Diagram (category theory), Directed set, Disjoint union, Domain of a function, Element (mathematics), Family of sets, Function (mathematics), Functor, If and only if, Image (mathematics), Index notation, Injective function, Integer, Intersection (set theory), Linear independence, Mathematical Society of Japan, Mathematics, Matrix (mathematics), Morphism, Multiset, Natural number, Net (mathematics), Ordered pair, Parametric family, Real number, Sequence, Set (mathematics), Surjective function, Tagged union, Tuple, Union (set theory).
Array data type
Language support for array types may include certain built-in array data types, some syntactic constructions (array type constructors) that the programmer may use to define such types and declare array variables, and special notation for indexing array elements.
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Cartesian product
In set theory (and, usually, in other parts of mathematics), a Cartesian product is a mathematical operation that returns a set (or product set or simply product) from multiple sets.
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Category theory
Category theory formalizes mathematical structure and its concepts in terms of a labeled directed graph called a category, whose nodes are called objects, and whose labelled directed edges are called arrows (or morphisms).
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Coproduct
In category theory, the coproduct, or categorical sum, is a category-theoretic construction which includes as examples the disjoint union of sets and of topological spaces, the free product of groups, and the direct sum of modules and vector spaces.
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Diagram (category theory)
In category theory, a branch of mathematics, a diagram is the categorical analogue of an indexed family in set theory.
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Directed set
In mathematics, a directed set (or a directed preorder or a filtered set) is a nonempty set A together with a reflexive and transitive binary relation ≤ (that is, a preorder), with the additional property that every pair of elements has an upper bound.
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Disjoint union
In set theory, the disjoint union (or discriminated union) of a family of sets is a modified union operation that indexes the elements according to which set they originated in.
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Domain of a function
In mathematics, and more specifically in naive set theory, the domain of definition (or simply the domain) of a function is the set of "input" or argument values for which the function is defined.
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Element (mathematics)
In mathematics, an element, or member, of a set is any one of the distinct objects that make up that set.
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Family of sets
In set theory and related branches of mathematics, a collection F of subsets of a given set S is called a family of subsets of S, or a family of sets over S. More generally, a collection of any sets whatsoever is called a family of sets.
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Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
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Functor
In mathematics, a functor is a map between categories.
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If and only if
In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements.
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Image (mathematics)
In mathematics, an image is the subset of a function's codomain which is the output of the function from a subset of its domain.
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Index notation
In mathematics and computer programming, index notation is used to specify the elements of an array of numbers.
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Injective function
In mathematics, an injective function or injection or one-to-one function is a function that preserves distinctness: it never maps distinct elements of its domain to the same element of its codomain.
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Integer
An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").
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Intersection (set theory)
In mathematics, the intersection A ∩ B of two sets A and B is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements.
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Linear independence
In the theory of vector spaces, a set of vectors is said to be if one of the vectors in the set can be defined as a linear combination of the others; if no vector in the set can be written in this way, then the vectors are said to be.
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Mathematical Society of Japan
The Mathematical Society of Japan (MSJ, 日本数学会) was the first academic society in Japan.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Matrix (mathematics)
In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.
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Morphism
In mathematics, a morphism is a structure-preserving map from one mathematical structure to another one of the same type.
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Multiset
In mathematics, a multiset (aka bag or mset) is a modification of the concept of a set that, unlike a set, allows for multiple instances for each of its elements.
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Natural number
In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").
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Net (mathematics)
In mathematics, more specifically in general topology and related branches, a net or Moore–Smith sequence is a generalization of the notion of a sequence.
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Ordered pair
In mathematics, an ordered pair (a, b) is a pair of objects.
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Parametric family
In mathematics and its applications, a parametric family or a parameterized family is a family of objects (a set of related objects) whose differences depend only on the chosen values for a set of parameters.
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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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Sequence
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed.
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Set (mathematics)
In mathematics, a set is a collection of distinct objects, considered as an object in its own right.
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Surjective function
In mathematics, a function f from a set X to a set Y is surjective (or onto), or a surjection, if for every element y in the codomain Y of f there is at least one element x in the domain X of f such that f(x).
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Tagged union
In computer science, a tagged union, also called a variant, variant record, choice type, discriminated union, disjoint union, or sum type, is a data structure used to hold a value that could take on several different, but fixed, types.
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Tuple
In mathematics, a tuple is a finite ordered list (sequence) of elements.
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Union (set theory)
In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection.
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Indexed families, Indexed family (mathematics), Indexed set.
References
[1] https://en.wikipedia.org/wiki/Indexed_family
