curve

The Hahn-Mazurkiewicz theorem is the following characterization of general continuous curves: A Hausdorff topological space is a continuous image of the unit interval if and only if it is a compact, connected, locally connected second-countable space. Note: In many formulations of the Hahn-Mazurkiewicz theorem, "second-countable" is replaced by "metrizable". These two formulations are equivalent. In one direction a compact Hausdorff space is a normal space and, by the Urysohn metrization theorem, second-countable then impli ...

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Space-filling curve, Space-filling curve - Outline of the construction of a space-filling curve, Space-filling curve - The Hahn-Mazurkiewicz theorem, Space-filling curve - Literature

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In keeping with the empirical perspective of this article the presentation focuses on the practical needs of an implementor of a technological subsystem embodying quaternion algebra. Typically, such subsystems are software systems executing on a digital computer. In contrast to a pure mathematician, a practitioner is always concerned with the low level detail of a representation, for these details ultimately determine whether a system works correctly or fails. Wherever possible, the details will be hidden by an abstraction which approaches a pre-existing mathematical ideal, but due to the finite nature of computin ...

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Quaternions and spatial rotation, Quaternions and spatial rotation - Introducion, Quaternions and spatial rotation - Non-commutativity, Quaternions and spatial rotation - Double covering, Quaternions and spatial rotation - Chirality, Quaternions and spatial rotation - Definitions, Quaternions and spatial rotation - Concepts, Quaternions and spatial rotation - Terminology, Quaternions and spatial rotation - Notation, Quaternions and spatial rotation - Reflections and Rotations, Quaternions and spatial rotation - Analytic form of a reflection, Quaternions and spatial rotation - Rotation: the composition of two reflections, Quaternions and spatial rotation - Quaternion representation of a rotation, Quaternions and spatial rotation - General rotations in four dimensional space, Quaternions and spatial rotation - Algebraic rules, Quaternions and spatial rotation - Other properties, Quaternions and spatial rotation - Quaternion rotation, Quaternions and spatial rotation - An example, Quaternions and spatial rotation - Quaternions versus other representations of rotations, Quaternions and spatial rotation - Pairs of unit quaternions as rotations in 4D space

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Quaternions and spatial rotation - Analytic form of a reflection. Quaternions and spatial rotation - Rotation: the composition of two reflections. Quaternions and spatial rotation - Quaternion representation of a rotation. Quaternions and spatial rotation - General rotations in four dimensional space. [This article is under reconstruction. The preceding text is in transition. The following text st ...

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Quaternions and spatial rotation, Quaternions and spatial rotation - Introducion, Quaternions and spatial rotation - Non-commutativity, Quaternions and spatial rotation - Double covering, Quaternions and spatial rotation - Chirality, Quaternions and spatial rotation - Definitions, Quaternions and spatial rotation - Concepts, Quaternions and spatial rotation - Terminology, Quaternions and spatial rotation - Notation, Quaternions and spatial rotation - Reflections and Rotations, Quaternions and spatial rotation - Analytic form of a reflection, Quaternions and spatial rotation - Rotation: the composition of two reflections, Quaternions and spatial rotation - Quaternion representation of a rotation, Quaternions and spatial rotation - General rotations in four dimensional space, Quaternions and spatial rotation - Algebraic rules, Quaternions and spatial rotation - Other properties, Quaternions and spatial rotation - Quaternion rotation, Quaternions and spatial rotation - An example, Quaternions and spatial rotation - Quaternions versus other representations of rotations, Quaternions and spatial rotation - Pairs of unit quaternions as rotations in 4D space

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Newton's law of universal gravitation states the following: Every point mass attracts every other point mass by a force directed along the line connecting the two. This force is proportional to the product of the masses and inversely proportional to the square of the distance between them: where: F is the magnitude of the (repulsive) gravitational force between the two point masses G is the gravitational constant m1 is the ma ...

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Gravity, Gravity - Overview of the history of gravitational theory, Gravity - Newton's law of universal gravitation, Gravity - Acceleration due to gravity, Gravity - Bodies with spatial extent, Gravity - Vector form, Gravity - Gravitational field, Gravity - The Earth's gravity, Gravity - Comparative gravities of the Earth Sun Moon and planets, Gravity - Mathematical equations for a falling body, Gravity - Gravitational potential, Gravity - Acceleration relative to the rotating Earth, Gravity - Gravity and astronomy, Gravity - Self-gravitating system, Gravity - Practical uses of gravity, Gravity - Problems with Newton's theory, Gravity - Theoretical concerns, Gravity - Disagreement with observation, Gravity - Newton's reservations, Gravity - Einstein's theory of gravitation, Gravity - Experimental tests, Gravity - Comparison with electromagnetic force, Gravity - Gravity and quantum mechanics, Gravity - Alternative theories, Gravity - Recent alternative theories, Gravity - Historical alternative theories, Gravity - Notes

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Gravity - Recent alternative theories. Brans-Dicke theory of gravity Rosen bi-metric theory of gravity In the modified Newtonian dynamics (MOND), Mordehai Milgrom proposes a modification of Newton's Second Law of motion for small accelerations. The new and "highly controversial" Process Physics theory attempts to address gravity Gravity - Historical alternative theories. Nikola Tesla challenged Albert Einstein's theory of relativity ...

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Gravity, Gravity - Overview of the history of gravitational theory, Gravity - Newton's law of universal gravitation, Gravity - Acceleration due to gravity, Gravity - Bodies with spatial extent, Gravity - Vector form, Gravity - Gravitational field, Gravity - The Earth's gravity, Gravity - Comparative gravities of the Earth Sun Moon and planets, Gravity - Mathematical equations for a falling body, Gravity - Gravitational potential, Gravity - Acceleration relative to the rotating Earth, Gravity - Gravity and astronomy, Gravity - Self-gravitating system, Gravity - Practical uses of gravity, Gravity - Problems with Newton's theory, Gravity - Theoretical concerns, Gravity - Disagreement with observation, Gravity - Newton's reservations, Gravity - Einstein's theory of gravitation, Gravity - Experimental tests, Gravity - Comparison with electromagnetic force, Gravity - Gravity and quantum mechanics, Gravity - Alternative theories, Gravity - Recent alternative theories, Gravity - Historical alternative theories, Gravity - Notes

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Although Newton's description of gravity is sufficiently accurate for many practical purposes, it suffers from several theoretical problems and is demonstrably not exactly correct. Gravity - Theoretical concerns. There is no prospect of identifying the mediator of gravity. Newton himself felt the inexplicable action at a distance to be unsatisfactory (see "Newton's reservations" below). Newton's theory requires that gravitational force is transmitted instantaneously. Given classical a ...

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Gravity, Gravity - Overview of the history of gravitational theory, Gravity - The Earth's gravity, Gravity - Comparative gravities of the Earth Sun Moon and planets, Gravity - Mathematical equations for a falling body, Gravity - Gravitational potential, Gravity - Acceleration relative to the rotating Earth, Gravity - Gravity and astronomy, Gravity - Self-gravitating system, Gravity - Practical uses of gravity, Gravity - Newton's law of universal gravitation, Gravity - Acceleration due to gravity, Gravity - Bodies with spatial extent, Gravity - Vector form, Gravity - Gravitational field, Gravity - Problems with Newton's theory, Gravity - Theoretical concerns, Gravity - Disagreement with observation, Gravity - Newton's reservations, Gravity - Einstein's theory of gravitation, Gravity - Experimental tests, Gravity - Comparison with electromagnetic force, Gravity - Gravity and quantum mechanics, Gravity - Alternative theories, Gravity - Recent alternative theories, Gravity - Historical alternative theories, Gravity - Notes

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Newton's law of universal gravitation states the following: Every point mass attracts every other point mass by a force directed along the line connecting the two. This force is proportional to the product of the masses and inversely proportional to the square of the distance between them: where: F is the magnitude of the (repulsive) gravitational force between the two point masses G is the gravitational constant m1 is the mass of t ...

See also:

Gravity, Gravity - Overview of the history of gravitational theory, Gravity - The Earth's gravity, Gravity - Comparative gravities of the Earth Sun Moon and planets, Gravity - Mathematical equations for a falling body, Gravity - Gravitational potential, Gravity - Acceleration relative to the rotating Earth, Gravity - Gravity and astronomy, Gravity - Self-gravitating system, Gravity - Practical uses of gravity, Gravity - Newton's law of universal gravitation, Gravity - Acceleration due to gravity, Gravity - Bodies with spatial extent, Gravity - Vector form, Gravity - Gravitational field, Gravity - Problems with Newton's theory, Gravity - Theoretical concerns, Gravity - Disagreement with observation, Gravity - Newton's reservations, Gravity - Einstein's theory of gravitation, Gravity - Experimental tests, Gravity - Comparison with electromagnetic force, Gravity - Gravity and quantum mechanics, Gravity - Alternative theories, Gravity - Recent alternative theories, Gravity - Historical alternative theories, Gravity - Notes

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Einstein's theory of gravitation answered the problems with Newton's theory noted above. In a revolutionary move, his theory of general relativity (1915) stated that the presence of mass, energy, and momentum causes spacetime to become curved. Because of this curvature, the paths that objects in inertial motion follow can "deviate" or change direction over time. This deviation appears to us as an acceleration towards massive objects, which Newton characterized as being gravity. In general relativity however, this acceleration or free-fall is ...

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Gravity, Gravity - Overview of the history of gravitational theory, Gravity - The Earth's gravity, Gravity - Comparative gravities of the Earth Sun Moon and planets, Gravity - Mathematical equations for a falling body, Gravity - Gravitational potential, Gravity - Acceleration relative to the rotating Earth, Gravity - Gravity and astronomy, Gravity - Self-gravitating system, Gravity - Practical uses of gravity, Gravity - Newton's law of universal gravitation, Gravity - Acceleration due to gravity, Gravity - Bodies with spatial extent, Gravity - Vector form, Gravity - Gravitational field, Gravity - Problems with Newton's theory, Gravity - Theoretical concerns, Gravity - Disagreement with observation, Gravity - Newton's reservations, Gravity - Einstein's theory of gravitation, Gravity - Experimental tests, Gravity - Comparison with electromagnetic force, Gravity - Gravity and quantum mechanics, Gravity - Alternative theories, Gravity - Recent alternative theories, Gravity - Historical alternative theories, Gravity - Notes

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The gravitational attraction between protons is approximately a factor of 1036 weaker than the electromagnetic repulsion. This factor is independent of distance, because both interactions are inversely proportional to the square of the distance. Therefore on an atomic scale mutual gravity is negligible. Even so, the main interaction between everyday objects and the Earth and between celestial bodies is gravity, because at this scale matter is electrically neutral. This means that there is an equal number of positively charged part ...

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Gravity, Gravity - Overview of the history of gravitational theory, Gravity - The Earth's gravity, Gravity - Comparative gravities of the Earth Sun Moon and planets, Gravity - Mathematical equations for a falling body, Gravity - Gravitational potential, Gravity - Acceleration relative to the rotating Earth, Gravity - Gravity and astronomy, Gravity - Self-gravitating system, Gravity - Practical uses of gravity, Gravity - Newton's law of universal gravitation, Gravity - Acceleration due to gravity, Gravity - Bodies with spatial extent, Gravity - Vector form, Gravity - Gravitational field, Gravity - Problems with Newton's theory, Gravity - Theoretical concerns, Gravity - Disagreement with observation, Gravity - Newton's reservations, Gravity - Einstein's theory of gravitation, Gravity - Experimental tests, Gravity - Comparison with electromagnetic force, Gravity - Gravity and quantum mechanics, Gravity - Alternative theories, Gravity - Recent alternative theories, Gravity - Historical alternative theories, Gravity - Notes

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It is widely believed that three of the four fundamental forces (the strong nuclear force, the weak nuclear force, and the electromagnetic force) are manifestations of a single, more fundamental force. Combining gravity with these forces of quantum mechanics to create a theory of quantum gravity is currently an important topic of research amongst physicists. General relativity is an essentially geometric theory that requires no exchange of particles in its explanation of gravity, whereas quantum mechanics relies on interactions betwee ...

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Gravity, Gravity - Overview of the history of gravitational theory, Gravity - The Earth's gravity, Gravity - Comparative gravities of the Earth Sun Moon and planets, Gravity - Mathematical equations for a falling body, Gravity - Gravitational potential, Gravity - Acceleration relative to the rotating Earth, Gravity - Gravity and astronomy, Gravity - Self-gravitating system, Gravity - Practical uses of gravity, Gravity - Newton's law of universal gravitation, Gravity - Acceleration due to gravity, Gravity - Bodies with spatial extent, Gravity - Vector form, Gravity - Gravitational field, Gravity - Problems with Newton's theory, Gravity - Theoretical concerns, Gravity - Disagreement with observation, Gravity - Newton's reservations, Gravity - Einstein's theory of gravitation, Gravity - Experimental tests, Gravity - Comparison with electromagnetic force, Gravity - Gravity and quantum mechanics, Gravity - Alternative theories, Gravity - Recent alternative theories, Gravity - Historical alternative theories, Gravity - Notes

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So Newton's original formula was: where the symbol means "is proportional to". To make this into an equal-sided formula or equation, there needed to be a multiplying factor or constant that would give the correct force of gravity no matter the value of the masses or distance between them. This gravitational constant was discovered in 1797 by Henry Cavendish. Thus the discovery and application of Newton's law of gravity accounts for the detailed information we have about the planets in our sol ...

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Gravity, Gravity - Overview of the history of gravitational theory, Gravity - The Earth's gravity, Gravity - Comparative gravities of the Earth Sun Moon and planets, Gravity - Mathematical equations for a falling body, Gravity - Gravitational potential, Gravity - Acceleration relative to the rotating Earth, Gravity - Gravity and astronomy, Gravity - Self-gravitating system, Gravity - Practical uses of gravity, Gravity - Newton's law of universal gravitation, Gravity - Acceleration due to gravity, Gravity - Bodies with spatial extent, Gravity - Vector form, Gravity - Gravitational field, Gravity - Problems with Newton's theory, Gravity - Theoretical concerns, Gravity - Disagreement with observation, Gravity - Newton's reservations, Gravity - Einstein's theory of gravitation, Gravity - Experimental tests, Gravity - Comparison with electromagnetic force, Gravity - Gravity and quantum mechanics, Gravity - Alternative theories, Gravity - Recent alternative theories, Gravity - Historical alternative theories, Gravity - Notes

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The equations below describe the motion of a falling body, assuming that the acceleration due to gravity is a constant, g (in which case Newton's law of gravitation simplifies to F = mg where m is the mass of the earth). This assumption is reasonable for objects falling to earth over the relatively short vertical distances of our everyday experience, but is very much untrue over larger distances (such as spacecraft trajectories). Galileo was the first to demonstrate and then formulate these equations. He used a ra ...

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Gravity, Gravity - Overview of the history of gravitational theory, Gravity - The Earth's gravity, Gravity - Comparative gravities of the Earth Sun Moon and planets, Gravity - Mathematical equations for a falling body, Gravity - Gravitational potential, Gravity - Acceleration relative to the rotating Earth, Gravity - Gravity and astronomy, Gravity - Self-gravitating system, Gravity - Practical uses of gravity, Gravity - Newton's law of universal gravitation, Gravity - Acceleration due to gravity, Gravity - Bodies with spatial extent, Gravity - Vector form, Gravity - Gravitational field, Gravity - Problems with Newton's theory, Gravity - Theoretical concerns, Gravity - Disagreement with observation, Gravity - Newton's reservations, Gravity - Einstein's theory of gravitation, Gravity - Experimental tests, Gravity - Comparison with electromagnetic force, Gravity - Gravity and quantum mechanics, Gravity - Alternative theories, Gravity - Recent alternative theories, Gravity - Historical alternative theories, Gravity - Notes

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E(1), E(2), and E(3) can be categorized as follows, with degrees of freedom: E(1) - 1: E+(1): identity - 0 translation - 1 those not preserving orientation: reflection in a point - 1 E(2) - 3: E+(2): identity - 0 translation - 2 rotation about a point - 3 those not preserving orientation: reflection in a line - 2 reflection in a line ...

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Euclidean group, Euclidean group - Subgroup structure matrix and vector representation, Euclidean group - Subgroups, Euclidean group - Relation to the affine group, Euclidean group - Rigid body motions, Euclidean group - Overview of isometries in up to three dimensions, Euclidean group - Commuting isometries, Euclidean group - Conjugacy classes

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The translations by a given distance in any direction form a conjugacy class; the translation group is the union of those for all distances. In 1D, all reflections are in the same class. In 2D, rotations by the same angle in either direction are in the same class. Glide reflections with translation by the same distance are in the same class. In 3D: Inversions with respect to all points are in the same class. Rotations by the same angle are in the same class. Rotations about an axis combined ...

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Euclidean group, Euclidean group - Subgroup structure matrix and vector representation, Euclidean group - Subgroups, Euclidean group - Relation to the affine group, Euclidean group - Rigid body motions, Euclidean group - Overview of isometries in up to three dimensions, Euclidean group - Commuting isometries, Euclidean group - Conjugacy classes

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The following year, Hernández came to the United States and began pitching in the Mariners' minor league system. In 2003, Hernández tore through Class-A with a 7-2 mark in Everett and Wisconsin. Returning to his native Venezuela to pitch in the winter league there, he held his own at 17 years of age against competition that included established major league players. Hernández was named the Mariners' minor league pitcher of the year in 2004, a season that also saw him make an appearance in the Futures Game. He started with Inland Em ...

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Félix Hernández, Félix Hernández - Discovery as a prospect, Félix Hernández - Minor league career, Félix Hernández - Major league debut

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The acceleration due to gravity at the Earth's surface, denoted g, is approximately 9.8 m/s2 (metres per second squared) or 32 ft/sec2. This means that, ignoring air resistance, an object falling freely near the earth's surface increases in speed by 9.8 m/s (around 22 mph) for each second of its descent. Thus, an object starting from rest will attain a speed of 9.8 m/s after one second, 19.6 m/s after two seconds, and so on. The earth itself experiences an equal and opposite force to that of the falling object, m ...

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Gravity, Gravity - Overview of the history of gravitational theory, Gravity - The Earth's gravity, Gravity - Comparative gravities of the Earth Sun Moon and planets, Gravity - Mathematical equations for a falling body, Gravity - Gravitational potential, Gravity - Acceleration relative to the rotating Earth, Gravity - Gravity and astronomy, Gravity - Self-gravitating system, Gravity - Practical uses of gravity, Gravity - Newton's law of universal gravitation, Gravity - Acceleration due to gravity, Gravity - Bodies with spatial extent, Gravity - Vector form, Gravity - Gravitational field, Gravity - Problems with Newton's theory, Gravity - Theoretical concerns, Gravity - Disagreement with observation, Gravity - Newton's reservations, Gravity - Einstein's theory of gravitation, Gravity - Experimental tests, Gravity - Comparison with electromagnetic force, Gravity - Gravity and quantum mechanics, Gravity - Alternative theories, Gravity - Recent alternative theories, Gravity - Historical alternative theories, Gravity - Notes

Read more here: » Gravity: Encyclopedia II - Gravity - The Earth's gravity

Gravity - Recent alternative theories. Brans-Dicke theory of gravity Rosen bi-metric theory of gravity In the modified Newtonian dynamics (MOND), Mordehai Milgrom proposes a modification of Newton's Second Law of motion for small accelerations. The new and "highly controversial" Process Physics theory attempts to address gravity Gravity - Historical alternative theories. Nikola Tesla challenged Albert Einstein's theory of relativity ...

See also:

Gravity, Gravity - Overview of the history of gravitational theory, Gravity - The Earth's gravity, Gravity - Comparative gravities of the Earth Sun Moon and planets, Gravity - Mathematical equations for a falling body, Gravity - Gravitational potential, Gravity - Acceleration relative to the rotating Earth, Gravity - Gravity and astronomy, Gravity - Self-gravitating system, Gravity - Practical uses of gravity, Gravity - Newton's law of universal gravitation, Gravity - Acceleration due to gravity, Gravity - Bodies with spatial extent, Gravity - Vector form, Gravity - Gravitational field, Gravity - Problems with Newton's theory, Gravity - Theoretical concerns, Gravity - Disagreement with observation, Gravity - Newton's reservations, Gravity - Einstein's theory of gravitation, Gravity - Experimental tests, Gravity - Comparison with electromagnetic force, Gravity - Gravity and quantum mechanics, Gravity - Alternative theories, Gravity - Recent alternative theories, Gravity - Historical alternative theories, Gravity - Notes

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A precise definition is required for the purposes of mathematics. A function is a binary relation, f, with the property that for an element x there is no more than one element y such that x is related to y. This uniquely determined element y is denoted f(x). Because two definitions of binary relation are in use, there are actually two definitions of function, in ...

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Function mathematics, Function mathematics - Mathematical definition of a function, Function mathematics - First definition, Function mathematics - Second definition, Function mathematics - History of the concept, Function mathematics - Functions in other fields, Function mathematics - The vocabulary of functions, Function mathematics - Specifying a function, Function mathematics - Functions with multiple inputs and outputs, Function mathematics - Functions of two or more variables, Function mathematics - Functions with output in a product set, Function mathematics - Binary operations, Function mathematics - Set of all functions, Function mathematics - Is a function more than its graph?, Function mathematics - Partial functions and multi-functions, Function mathematics - Other properties, Function mathematics - Restrictions and extensions, Function mathematics - Pointwise operations, Function mathematics - Computable and non-computable functions, Function mathematics - Lambda calculus, Function mathematics - Functions in category theory

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Informally, a restriction of a function f is the result of trimming its graph to a smaller domain. More precisely, if f is a function from a X to Y, and S is any subset of X, the restriction of f to S is the function f|S from S to Y such that f|S(s) = f(s) for all s in S. The restriction f|S can also be expressed as the composition f incS,X, where incSSee also:

Function mathematics, Function mathematics - Mathematical definition of a function, Function mathematics - First definition, Function mathematics - Second definition, Function mathematics - History of the concept, Function mathematics - Functions in other fields, Function mathematics - The vocabulary of functions, Function mathematics - Specifying a function, Function mathematics - Functions with multiple inputs and outputs, Function mathematics - Functions of two or more variables, Function mathematics - Functions with output in a product set, Function mathematics - Binary operations, Function mathematics - Set of all functions, Function mathematics - Is a function more than its graph?, Function mathematics - Partial functions and multi-functions, Function mathematics - Other properties, Function mathematics - Restrictions and extensions, Function mathematics - Pointwise operations, Function mathematics - Computable and non-computable functions, Function mathematics - Lambda calculus, Function mathematics - Functions in category theory

Read more here: » Function mathematics: Encyclopedia II - Function mathematics - Restrictions and extensions

The condition for a binary relation f from X to Y to be a function can be split into two conditions: f is total, or entire: for each x in X, there exists some y in Y such that x is related to y. f is single-valued: for each x in X, there is at most one y in Y such that x is related to y. In some contexts, a relation that satisfies condition (1), but not necessarily (2) ...

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Function mathematics, Function mathematics - Mathematical definition of a function, Function mathematics - First definition, Function mathematics - Second definition, Function mathematics - History of the concept, Function mathematics - Functions in other fields, Function mathematics - The vocabulary of functions, Function mathematics - Specifying a function, Function mathematics - Functions with multiple inputs and outputs, Function mathematics - Functions of two or more variables, Function mathematics - Functions with output in a product set, Function mathematics - Binary operations, Function mathematics - Set of all functions, Function mathematics - Is a function more than its graph?, Function mathematics - Partial functions and multi-functions, Function mathematics - Other properties, Function mathematics - Restrictions and extensions, Function mathematics - Pointwise operations, Function mathematics - Computable and non-computable functions, Function mathematics - Lambda calculus, Function mathematics - Functions in category theory

Read more here: » Function mathematics: Encyclopedia II - Function mathematics - Partial functions and multi-functions

If f: X → R and g: X → R are functions with common domain X and codomain is a ring R, then one can define the sum function f + g: X → R and the product function f × g: X → R as follows: (f + g)(x) = f(x) + g(x) (f × g)(x) = f(x) × < ...

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Function mathematics, Function mathematics - Mathematical definition of a function, Function mathematics - First definition, Function mathematics - Second definition, Function mathematics - History of the concept, Function mathematics - Functions in other fields, Function mathematics - The vocabulary of functions, Function mathematics - Specifying a function, Function mathematics - Functions with multiple inputs and outputs, Function mathematics - Functions of two or more variables, Function mathematics - Functions with output in a product set, Function mathematics - Binary operations, Function mathematics - Set of all functions, Function mathematics - Is a function more than its graph?, Function mathematics - Partial functions and multi-functions, Function mathematics - Other properties, Function mathematics - Restrictions and extensions, Function mathematics - Pointwise operations, Function mathematics - Computable and non-computable functions, Function mathematics - Lambda calculus, Function mathematics - Functions in category theory

Read more here: » Function mathematics: Encyclopedia II - Function mathematics - Pointwise operations

The notion of function is generalizes to the notion of morphism in the context of category theory. A category is a collection of objects and morphisms, each morphism is an ordered triple (X, Y, f), where f is a rule connecting domain X and codomain Y, and X and Y are objects in the collection. Ordinary functions are sometimes referred to as morphisms in a concrete category. ...

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Function mathematics, Function mathematics - Mathematical definition of a function, Function mathematics - First definition, Function mathematics - Second definition, Function mathematics - History of the concept, Function mathematics - Functions in other fields, Function mathematics - The vocabulary of functions, Function mathematics - Specifying a function, Function mathematics - Functions with multiple inputs and outputs, Function mathematics - Functions of two or more variables, Function mathematics - Functions with output in a product set, Function mathematics - Binary operations, Function mathematics - Set of all functions, Function mathematics - Is a function more than its graph?, Function mathematics - Partial functions and multi-functions, Function mathematics - Other properties, Function mathematics - Restrictions and extensions, Function mathematics - Pointwise operations, Function mathematics - Computable and non-computable functions, Function mathematics - Lambda calculus, Function mathematics - Functions in category theory

Read more here: » Function mathematics: Encyclopedia II - Function mathematics - Functions in category theory