## Metric Mathematics Wikipedia

### Metric (mathematics) - Wikipedia.

In mathematics, a metric or distance function is a function that gives a distance between each pair of point elements of a set.A set with a metric is a metric space. A metric induces a topology on a set, but not all topologies can be generated by a metric. A topological space whose topology can be described by a metric is a metrizable space.. One important source of metrics in ....

https://en.wikipedia.org/wiki/Metric_(mathematics).

### Metric - Wikipedia.

Mathematics. Metric (mathematics), an abstraction of the notion of distance in a metric space Metric tensor, in differential geometry, the distance structure on a manifold; Physics. Metric tensor (general relativity), the fundamental object of study in general relativity similar to the gravitational field in Newtonian physics Metric system, an internationally adopted decimal ....

https://en.wikipedia.org/wiki/Metric.

### Metric space - Wikipedia.

In mathematics, a metric space is a set together with a metric on the set. The metric is a function that defines a concept of distance between any two members of the set, which are usually called points.The metric satisfies the following properties: the distance from A to B is zero if and only if A and B are the same point,; the distance between two distinct points is positive,.

https://en.wikipedia.org/wiki/Metric_space.

### Metrication in the United Kingdom - Wikipedia.

Metrication in the United Kingdom, the process of introducing the metric system of measurement in place of imperial units, has made steady progress since the mid-20th century but today remains equivocal and varies by context.Most of government, industry and commerce use metric units, but imperial units are officially used to specify journey distances, vehicle speeds and the sizes of ....

https://en.wikipedia.org/wiki/Metrication_in_the_United_Kingdom.

### Teichmüller space - Wikipedia.

In mathematics, the Teichmuller space of a (real) topological (or differential) surface, is a space that parametrizes complex structures on up to the action of homeomorphisms that are isotopic to the identity homeomorphism.Teichmuller spaces are named after Oswald Teichmuller.. Each point in a Teichmuller space () may be regarded as an isomorphism class of "marked" Riemann ....

https://en.wikipedia.org/wiki/Teichm%C3%BCller_space.

### Isometry - Wikipedia.

Introduction. Given a metric space (loosely, a set and a scheme for assigning distances between elements of the set), an isometry is a transformation which maps elements to the same or another metric space such that the distance between the image elements in the new metric space is equal to the distance between the elements in the original metric space..

https://en.wikipedia.org/wiki/Isometry.

### Tensor calculus - Wikipedia.

In mathematics, tensor calculus, tensor analysis, or Ricci calculus is an extension of vector calculus to tensor fields (tensors that may vary over a manifold, e.g. in spacetime).. Developed by Gregorio Ricci-Curbastro and his student Tullio Levi-Civita, it was used by Albert Einstein to develop his general theory of relativity.Unlike the infinitesimal calculus, tensor calculus allows ....

https://en.wikipedia.org/wiki/Tensor_calculus.

### Alcubierre drive - Wikipedia.

The Alcubierre drive is a speculative warp drive idea according to which a spacecraft could achieve apparent faster-than-light travel by contracting space in front of it and expanding space behind it, under the assumption that a configurable energy-density field lower than that of vacuum (that is, negative mass) could be created. Proposed by theoretical physicist Miguel Alcubierre ....

https://en.wikipedia.org/wiki/Alcubierre_drive.

### Discrete space - Wikipedia.

In 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 ....

https://en.wikipedia.org/wiki/Discrete_space.

### Mathematical structure - Wikipedia.

In mathematics, a structure is a set endowed with some additional features on the set (e.g. an operation, relation, metric, or topology).Often, the additional features are attached or related to the set, so as to provide it with some additional meaning or significance. A partial list of possible structures are measures, algebraic structures (groups, fields, etc.), topologies, metric ....

https://en.wikipedia.org/wiki/Mathematical_structure.

### Circle - Wikipedia.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant.The distance between any point of the circle and the centre is called the radius.Usually, the radius is required to be a positive number..

https://en.wikipedia.org/wiki/Circle.

### Glossary of areas of mathematics - Wikipedia.

Mathematics is a broad subject that is commonly divided in many areas that may be defined by their objects of study, by the used methods, or by both. For example, analytic number theory is a subarea of number theory devoted to the use of methods of analysis for the study of natural numbers. This glossary is alphabetically sorted. This hides a large part of the relationships ....

https://en.wikipedia.org/wiki/Glossary_of_areas_of_mathematics.

### Hash function - Wikipedia.

A universal hashing scheme is a randomized algorithm that selects a hashing function h among a family of such functions, in such a way that the probability of a collision of any two distinct keys is 1/m, where m is the number of distinct hash values desired--independently of the two keys. Universal hashing ensures (in a probabilistic sense) that the hash function application will ....

https://en.wikipedia.org/wiki/Hash_function.

### Letter case - Wikipedia.

Letter case is the distinction between the letters that are in larger uppercase or capitals (or more formally majuscule) and smaller lowercase (or more formally minuscule) in the written representation of certain languages.The writing systems that distinguish between the upper and lowercase have two parallel sets of letters, with each letter in one set usually having an ....

https://en.wikipedia.org/wiki/Letter_case.

### Cooking weights and measures - Wikipedia.

Metric measures. In most of the world, recipes use the metric system of units--litres (L) and millilitres (mL), grams (g) and kilograms (kg), and degrees Celsius (?C). The official spelling litre is used in most English-speaking nations; the notable exception is the United States where the spelling liter is preferred.. The United States measures weight in pounds (avoirdupois), while ....

https://en.wikipedia.org/wiki/Cooking_weights_and_measures.

### Moment (mathematics) - Wikipedia.

In mathematics, the moments of a function are quantitative measures related to the shape of the function's graph.If the function represents mass density, then the zeroth moment is the total mass, the first moment (normalized by total mass) is the centre of mass, and the second moment is the moment of inertia.If the function is a probability distribution, then the first moment is the ....

https://en.wikipedia.org/wiki/Moment_(mathematics).

### Series (mathematics) - Wikipedia.

In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity. The study of series is a major part of calculus and its generalization, mathematical analysis.Series are used in most areas of mathematics, even for studying finite structures (such as in combinatorics) through generating ....

https://en.wikipedia.org/wiki/Series_(mathematics).

### Dense set - Wikipedia.

Definition. A subset of a topological space is said to be a dense subset of if any of the following equivalent conditions are satisfied: . The smallest closed subset of containing is itself.; The closure of in is equal to . That is, =. The interior of the complement of is empty. That is, =. Every point in either belongs to or is a limit point of .; For every , every neighborhood of ....

https://en.wikipedia.org/wiki/Dense_set.

### Value at risk - Wikipedia.

Details. Common parameters for VaR are 1% and 5% probabilities and one day and two week horizons, although other combinations are in use. The reason for assuming normal markets and no trading, and to restricting loss to things measured in daily accounts, is to make the loss observable.In some extreme financial events it can be impossible to determine losses, either ....

https://en.wikipedia.org/wiki/Value_at_risk.

### Continuous function - Wikipedia.

In mathematics, a continuous function is a function such that a continuous variation (that is a change without jump) of the argument induces a continuous variation of the value of the function. This means that there are no abrupt changes in value, known as discontinuities.More precisely, a function is continuous if arbitrarily small changes in its value can be assured by restricting to ....

https://en.wikipedia.org/wiki/Continuous_function.

### Space (mathematics) - Wikipedia.

In ancient Greek mathematics, "space" was a geometric abstraction of the three-dimensional reality observed in everyday life. About 300 BC, Euclid gave axioms for the properties of space. Euclid built all of mathematics on these geometric foundations, going so far as to define numbers by comparing the lengths of line segments to the length of a chosen reference segment..

https://en.wikipedia.org/wiki/Space_(mathematics).