Discrete spaceIn topology, a discrete space is a particularly simple example of a topological space or similar structure, one in which the points form a discontinuous sequence, meaning they are isolated from each other in a certain sense. The discrete topology is the finest topology that can be given on a set. Every subset is open in the discrete topology so that in particular, every singleton subset is an open set in the discrete topology.
Set (mathematics)In mathematics, a set is a collection of different things; the things are called elements or members of the set and are typically mathematical objects: numbers, symbols, points in space, lines, other geometric shapes, variables, functions, or even other sets. Mathematics typically does not define precisely what constitutes a "set" or "collection", because such a definition would have to be in terms of something else previously defined.
SubsetIn mathematics, a setA is a subset of a set Bif and only 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). A is a subset of B may also be expressed as B includes (or contains) A or A is included (or contained) in B. A k-subset is a subset with k elements.
Rooted graphIn mathematics, and, in particular, in graph theory, a rooted graph is a graph in which one vertex has been distinguished as the root. Both directed and undirected versions of rooted graphs have been studied, and there are also variant definitions that allow multiple roots. Rooted graphs may also be known (depending on their application) as pointed graphs or flow graphs.TupleIn mathematics, a tuple is a finite sequence (or ordered list) of numbers. More generally, it is a sequence of mathematical objects, called the elements of the tuple. An n-tuple is a tuple of n elements, where n is a non-negative integer. There is only one 0-tuple, called the empty tuple. A 1-tuple and a 2-tuple are commonly called a singleton and an ordered pair, respectively. The term "infinite tuple" is occasionally used for "infinite sequences".
Computer scienceStudy of computationFundamental areas of computer scienceProgramming language theoryComputer architectureArtificial intelligenceComputational complexity theoryComputer science is the study of computation, information, and automation, together with their associated phenomena.
Game theoryMathematical models of strategic interactionsGame theory is the field of applied mathematics that models interactions between multiple agents as "games" of strategy between "players". It is a scientific method of describing, predicting, evaluating, and selecting choices (or "actions"), often with the view of maximising utility outcomes (or "payoffs") for one or more players.
Continuous functionMathematical function with no sudden changes
PendulumMechanism for regulating the speed of clocks"Simple gravity pendulum" model assumes no friction or air resistance.A pendulum is a mechanical device consisting of a weight suspended from a pivot so that it can swing freely. When a pendulum is displaced sideways from its resting mechanical equilibrium position, it is subject to a restoring force due to gravity, which will accelerate it back toward the equilibrium position.
Artificial intelligenceIntelligence in machinesArtificial intelligence (AI) is the capability of computational systems to perform tasks typically associated with human intelligence, such as learning, reasoning, problem-solving, perception, and decision-making.
Toy problemIn scientific disciplines, a toy problem or a puzzlelike problem is a problem that is not of immediate scientific interest, yet is used as an expository device to illustrate a trait that may be shared by other, more complicated, instances of the problem, or as a way to explain a particular, more general, problem solving technique. A toy problem is useful to test and demonstrate methodologies. Researchers can use toy problems to compare the performance of different algorithms.
Natural numberNatural numbers can be used for counting: one apple plus two apples equals three apples.In mathematics, the natural numbers are the numbers used for counting up, starting from 0 or 1. The first few natural numbers are 0 (if included), 1, 2, 3, and so on. The terms positive integers, non-negative integers, whole numbers, and counting numbers are also used. The set of the natural numbers is commonly denoted by a bold N or a blackboard boldN{\displaystyle \mathbb {N} }.
Set (mathematics)In mathematics, a set is a collection of different things; the things are called elements or members of the set and are typically mathematical objects: numbers, symbols, points in space, lines, other geometric shapes, variables, functions, or even other sets. Mathematics typically does not define precisely what constitutes a "set" or "collection", because such a definition would have to be in terms of something else previously defined.SubsetIn mathematics, a setA is a subset of a set Bif and only 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). A is a subset of B may also be expressed as B includes (or contains) A or A is included (or contained) in B. A k-subset is a subset with k elements.Rooted graphIn mathematics, and, in particular, in graph theory, a rooted graph is a graph in which one vertex has been distinguished as the root. Both directed and undirected versions of rooted graphs have been studied, and there are also variant definitions that allow multiple roots. Rooted graphs may also be known (depending on their application) as pointed graphs or flow graphs.TupleIn mathematics, a tuple is a finite sequence (or ordered list) of numbers. More generally, it is a sequence of mathematical objects, called the elements of the tuple. An n-tuple is a tuple of n elements, where n is a non-negative integer. There is only one 0-tuple, called the empty tuple. A 1-tuple and a 2-tuple are commonly called a singleton and an ordered pair, respectively. The term "infinite tuple" is occasionally used for "infinite sequences".Computer scienceStudy of computationFundamental areas of computer scienceProgramming language theoryComputer architectureArtificial intelligenceComputational complexity theoryComputer science is the study of computation, information, and automation, together with their associated phenomena.Game theoryMathematical models of strategic interactionsGame theory is the field of applied mathematics that models interactions between multiple agents as "games" of strategy between "players". It is a scientific method of describing, predicting, evaluating, and selecting choices (or "actions"), often with the view of maximising utility outcomes (or "payoffs") for one or more players.Continuous functionMathematical function with no sudden changesPendulumMechanism for regulating the speed of clocks"Simple gravity pendulum" model assumes no friction or air resistance.A pendulum is a mechanical device consisting of a weight suspended from a pivot so that it can swing freely. When a pendulum is displaced sideways from its resting mechanical equilibrium position, it is subject to a restoring force due to gravity, which will accelerate it back toward the equilibrium position.Artificial intelligenceIntelligence in machinesArtificial intelligence (AI) is the capability of computational systems to perform tasks typically associated with human intelligence, such as learning, reasoning, problem-solving, perception, and decision-making.Toy problemIn scientific disciplines, a toy problem or a puzzlelike problem is a problem that is not of immediate scientific interest, yet is used as an expository device to illustrate a trait that may be shared by other, more complicated, instances of the problem, or as a way to explain a particular, more general, problem solving technique. A toy problem is useful to test and demonstrate methodologies. Researchers can use toy problems to compare the performance of different algorithms.Natural numberNatural numbers can be used for counting: one apple plus two apples equals three apples.In mathematics, the natural numbers are the numbers used for counting up, starting from 0 or 1. The first few natural numbers are 0 (if included), 1, 2, 3, and so on. The terms positive integers, non-negative integers, whole numbers, and counting numbers are also used. The set of the natural numbers is commonly denoted by a bold N or a blackboard boldN{\displaystyle \mathbb {N} }.*As an Amazon Associate I earn from qualifying purchases.