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Multiplicative Inverse
In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and their changes (cal ..., a multiplicative inverse or reciprocal for a number ''x'', denoted by 1/''x'' or ''x''−1, is a number which when multiplied by ''x'' yields the multiplicative identity In mathematics, an identity element, or neutral element, is a special type of element of a set with respect to a binary operation on that set, which leaves any element of the set unchanged when combined with it. This concept is used in algebraic s ..., 1. The multiplicative inverse of a fraction A fraction (from Latin ', "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths .. ...
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Hyperbola One Over X
In mathematics, a hyperbola () (adjective form hyperbolic, ) (plural ''hyperbolas'', or ''hyperbolae'' ()) is a type of smooth function, smooth plane curve, 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 component (graph theory), connected components or branches, that are mirror images of each other and resemble two infinite bow (weapon), bows. The hyperbola is one of the three kinds of conic section, formed by the intersection of a plane (mathematics), plane and a double cone (geometry), 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. Hyperbolas arise in many ways: * as the curve representing the function (mathematics), function y(x) = 1/x in the Cartesian coordinate system, C ...
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French Language
French ( or ) is a Romance language The Romance languages, less commonly Latin or Neo-Latin languages, are the modern languages that evolved from Vulgar Latin Vulgar Latin, also known as Popular or Colloquial Latin is a range of informal sociolects of Latin Latin (, or , ) ... of the Indo-European family The Indo-European languages are a language family A language is a structured system of communication used by humans, including speech ( spoken language), gestures (Signed language, sign language) and writing. Most languages have a writing .... It descended from the Vulgar Latin Vulgar Latin, also known as Popular or Colloquial Latin, is non-literary Literature broadly is any collection of written work, but it is also used more narrowly for writings specifically considered to be an art form, especially prose fiction, ... of the Roman Empire The Roman Empire ( la, Imperium Rōmānum ; grc-gre, Βασιλεία τῶν Ῥωμαίων, Bas ...
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Sedenion
In abstract algebra In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures. Algebraic structures include group (mathematics), groups, ring (mathematics), rings, field (mathema ..., the sedenions form a 16-dimensional File:Dimension levels.svg, thumb , 236px , The first four spatial dimensions, represented in a two-dimensional picture. In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum numb ... noncommutative In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). I ... and nonassociative In mathematics, the associative property is a property of some binary operations, which means that rearranging the parentheses in an express ...
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Coprime
In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and their changes (cal ..., two integer An integer (from the Latin Latin (, or , ) is a classical language A classical language is a language A language is a structured system of communication Communication (from Latin ''communicare'', meaning "to share" or "to ...s and are coprime, relatively prime or mutually prime if the only positive integer that is a divisor In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities a ... of both of them is 1. Consequently, any prime number A prime number (or a prime) is a natural numbe ...
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If And Only If
In logic Logic is an interdisciplinary field which studies truth and reasoning. Informal logic seeks to characterize Validity (logic), valid arguments informally, for instance by listing varieties of fallacies. Formal logic represents statements and ar ... and related fields such as mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and their changes (cal ... and philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about Metaphysics, existence, reason, Epistemology, knowledge, Ethics, values, Philosophy of mind, mind, and Philosophy of language, language. Such questio ..., "if and only if" (shortened as "iff") is a biconditional In logic Logic (from Ancient Greek, Greek: grc, wikt:λογική, λογική, label=none, lit=pos ...
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Modular Multiplicative Inverse
In mathematics, particularly in the area of arithmetic, a modular multiplicative inverse of an integer is an integer such that the product is Congruence relation#Basic example, congruent to 1 with respect to the modulus .. In the standard notation of modular arithmetic this congruence is written as :ax \equiv 1 \pmod, which is the shorthand way of writing the statement that divides (evenly) the quantity , or, put another way, the remainder after dividing by the integer is 1. If does have an inverse modulo , then there are an infinite number of solutions of this congruence, which form a modular arithmetic#Congruence classes, congruence class with respect to this modulus. Furthermore, any integer that is congruent to (i.e., in 's congruence class) has any element of 's congruence class as a modular multiplicative inverse. Using the notation of \overline to indicate the congruence class containing , this can be expressed by saying that the ''modulo multiplicative inverse'' of the ...
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Modular Arithmetic
#REDIRECT Modular arithmetic #REDIRECT Modular arithmetic#REDIRECT Modular arithmetic In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), a ...
{{R from other capitalisation ...
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Integer
An integer (from the Latin Latin (, or , ) is a classical language A classical language is a language A language is a structured system of communication Communication (from Latin ''communicare'', meaning "to share" or "to be in relation with") is "an appa ... ''integer'' meaning "whole") is colloquially defined as a number A number is a mathematical object A mathematical object is an abstract concept arising in mathematics. In the usual language of mathematics, an ''object'' is anything that has been (or could be) formally defined, and with which one may do deduct ... that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, , and  are not. The set of integers consists of zero (), the positive natural number In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and total order, ordering (as in "this is the ''third'' larges ...
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Field (mathematics)
In mathematics, a field is a set (mathematics), set on which addition, subtraction, multiplication, and division (mathematics), division are defined and behave as the corresponding operations on rational number, rational and real numbers do. A field is thus a fundamental algebraic structure which is widely used in algebra, number theory, and many other areas of mathematics. The best known fields are the field of rational numbers, the field of real numbers and the field of complex numbers. Many other fields, such as field of rational functions, fields of rational functions, algebraic function fields, algebraic number fields, and p-adic number, ''p''-adic fields are commonly used and studied in mathematics, particularly in number theory and algebraic geometry. Most cryptographic protocols rely on finite fields, i.e., fields with finitely many element (set), elements. The relation of two fields is expressed by the notion of a field extension. Galois theory, initiated by Évariste ...
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Complex Number
In mathematics, a complex number is an element of a number system that contains the real numbers and a specific element denoted , called the imaginary unit, and satisfying the equation . Moreover, every complex number can be expressed in the form , where and are real numbers. Because no real number satisfies the above equation, was called an imaginary number by René Descartes. For the complex number , is called the and is called the . The set of complex numbers is denoted by either of the symbols \mathbb C or . Despite the historical nomenclature "imaginary", complex numbers are regarded in the mathematical sciences as just as "real" as the real numbers and are fundamental in many aspects of the scientific description of the natural world. Complex numbers allow solutions to all polynomial equations, even those that have no solutions in real numbers. More precisely, the fundamental theorem of algebra asserts that every non-constant polynomial equation with real or complex c ...
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Real Number
In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained (), and quantities and their changes ( and ). There is no general consensus abo ..., a real number is a value of a continuous quantity Quantity is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value in terms of a unit of measu ... that can represent a distance along a line Line, lines, The Line, or LINE may refer to: Arts, entertainment, and media Films * ''Lines'' (film), a 2016 Greek film * ''The Line'' (2017 film) * ''The Line'' (2009 film) * ''The Line'', a 2009 independent film by Nancy Schwartzman Lite ... (or alternatively, a quantity that can be represented as an infinite decimal expansion). The adjective ''real'' in this co ...
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