Multiplicative inverse in the context of "Unit (ring theory)"

In mathematics, a hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows. The hyperbola is one of the three kinds of conic section, formed by the intersection of a plane and a double cone. (The other conic sections are the parabola and the ellipse. A circle is a special case of an ellipse.) If the plane intersects both halves of the double cone but does not pass through the apex of the cones, then the conic is a hyperbola.

Besides being a conic section, a hyperbola can arise as the locus of points whose difference of distances to two fixed foci is constant, as a curve for each point of which the rays to two fixed foci are reflections across the tangent line at that point, or as the solution of certain bivariate quadratic equations such as the reciprocal relationship ${\displaystyle xy=1.}$ In practical applications, a hyperbola can arise as the path followed by the shadow of the tip of a sundial's gnomon, the shape of an open orbit such as that of a celestial object exceeding the escape velocity of the nearest gravitational body, or the scattering trajectory of a subatomic particle, among others.

The foreign exchange market (forex, FX, or currency market) is a global decentralized or over-the-counter (OTC) market for the trading of currencies. This market determines foreign exchange rates for every currency. By trading volume, it is by far the largest market in the world, followed by the credit market.

The main participants are the larger international banks. Financial centres function as anchors of trading between a range of multiple types of buyers and sellers around the clock, with the exception of weekends. As currencies are always traded in pairs, the market does not set a currency's absolute value, but rather determines its relative value by setting the market price of one currency if paid for with another. Example: 1 USD is worth 1.1 Euros or 1.2 Swiss Francs etc. The market works through financial institutions and operates on several levels. Behind the scenes, banks turn to a smaller number of financial firms known as "dealers", who are involved in large quantities of trading. Most foreign exchange dealers are banks, so this behind-the-scenes market is sometimes called the "interbank market". Trades between dealers can be very large, involving hundreds of millions of dollars. Because of the sovereignty issue when involving two currencies, Forex has little supervisory entity regulating its actions. In a typical foreign exchange transaction, a party purchases some quantity of one currency by paying with some quantity of another currency.

In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. In other words, it is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, troughs, or zero crossings. Wavelength is a characteristic of both traveling waves and standing waves, as well as other spatial wave patterns. The inverse of the wavelength is called the spatial frequency. Wavelength is commonly designated by the Greek letter lambda (λ). For a modulated wave, wavelength may refer to the carrier wavelength of the signal. The term wavelength may also apply to the repeating envelope of modulated waves or waves formed by interference of several sinusoids.

Assuming a sinusoidal wave moving at a fixed wave speed, wavelength is inversely proportional to the frequency of the wave: waves with higher frequencies have shorter wavelengths, and lower frequencies have longer wavelengths.

Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio signals (sound), radio waves, and light.

The interval of time between events is called the period. It is the reciprocal of the frequency. For example, if a heart beats at a frequency of 120 times per minute (2 hertz), its period is one half of a second.

An f-number is a measure of the light-gathering ability of an optical system such as a camera lens. It is defined as the ratio of the system's focal length to the diameter of the entrance pupil ("clear aperture"). The f-number is also known as the focal ratio, f-ratio, or f-stop, and it is key in determining the depth of field, diffraction, and exposure of a photograph. The f-number is dimensionless and is usually expressed using a lower-case hooked f with the format f/N, where N is the f-number.

The f-number is also known as the inverse relative aperture, because it is the inverse of the relative aperture, defined as the aperture diameter divided by the focal length. A lower f-number means a larger relative aperture and more light entering the system, while a higher f-number means a smaller relative aperture and less light entering the system. The f-number is related to the numerical aperture (NA) of the system, which measures the range of angles over which light can enter or exit the system. The numerical aperture takes into account the refractive index of the medium in which the system is working, while the f-number does not.

One half is the multiplicative inverse of 2. It is an irreducible fraction with a numerator of 1 and a denominator of 2. It often appears in mathematical equations, recipes and measurements.

The energy efficiency in transport is the useful travelled distance, of passengers, goods or any type of load; divided by the total energy put into the transport propulsion means. The energy input might be rendered in several different types depending on the type of propulsion, and normally such energy is presented in liquid fuels, electrical energy or food energy. The energy efficiency is also occasionally known as energy intensity. The inverse of the energy efficiency in transport is the energy consumption in transport.

Energy efficiency in transport is often described in terms of fuel consumption, fuel consumption being the reciprocal of fuel economy. Nonetheless, fuel consumption is linked with a means of propulsion which uses liquid fuels, whilst energy efficiency is applicable to any sort of propulsion. To avoid said confusion, and to be able to compare the energy efficiency in any type of vehicle, experts tend to measure the energy in the International System of Units, i.e., joules.

In mathematics, an infinitesimal number is a non-zero quantity that is closer to 0 than any non-zero real number is. The word infinitesimal comes from a 17th-century Modern Latin coinage infinitesimus, which originally referred to the "infinitieth" item in a sequence.

Infinitesimals do not exist in the standard real number system, but they do exist in other number systems, such as the surreal number system and the hyperreal number system, which can be thought of as the real numbers augmented with both infinitesimal and infinite quantities; the augmentations are the reciprocals of one another.

In mathematics, an operation is a function from a set to itself. For example, an operation on real numbers will take in real numbers and return a real number. An operation can take zero or more input values (also called "operands" or "arguments") to a well-defined output value. The number of operands is the arity of the operation.

The most commonly studied operations are binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse. An operation of arity zero, or nullary operation, is a constant. The mixed product is an example of an operation of arity 3, also called ternary operation.