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# Number

A number is a mathematical object used to count, measure and also label. [1]

## Abel–Ruffini theorem

In algebra, the Abel–Ruffini theorem (also known as Abel's impossibility theorem) states that there is no algebraic solution—that is, solution in radicals—to the general polynomial equations of degree five or higher with arbitrary coefficients.

## Abraham de Moivre

Abraham de Moivre (26 May 166727 November 1754) was a French mathematician known for de Moivre's formula, a formula that links complex numbers and trigonometry, and for his work on the normal distribution and probability theory.

## Abraham Robinson

Abraham Robinson (born Robinsohn; October 6, 1918 – April 11, 1974) was a mathematician who is most widely known for development of non-standard analysis, a mathematically rigorous system whereby infinitesimal and infinite numbers were reincorporated into modern mathematics.

## Absolute value

In mathematics, the absolute value or modulus of a real number is the non-negative value of without regard to its sign.

## Abstraction (mathematics)

Abstraction in mathematics is the process of extracting the underlying essence of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena.

## Actual infinity

In the philosophy of mathematics, the abstraction of actual infinity involves the acceptance (if the axiom of infinity is included) of infinite entities, such as the set of all natural numbers or an infinite sequence of rational numbers, as given, actual, completed objects.

Addition (often signified by the plus symbol "+") is one of the four basic operations of arithmetic; the others are subtraction, multiplication and division.

Adrien-Marie Legendre (18 September 1752 – 10 January 1833) was a French mathematician.

Alfred North Whitehead (15 February 1861 – 30 December 1947) was an English mathematician and philosopher.

## Algebraic function field

In mathematics, an (algebraic) function field of n variables over the field k is a finitely generated field extension K/k which has transcendence degree n over k. Equivalently, an algebraic function field of n variables over k may be defined as a finite field extension of the field K.

## Algebraic integer

In algebraic number theory, an algebraic integer is a complex number that is a root of some monic polynomial (a polynomial whose leading coefficient is 1) with coefficients in (the set of integers).

## Algebraic number

An algebraic number is any complex number (including real numbers) that is a root of a non-zero polynomial (that is, a value which causes the polynomial to equal 0) in one variable with rational coefficients (or equivalently – by clearing denominators – with integer coefficients).

## Algebraically closed field

In abstract algebra, an algebraically closed field F contains a root for every non-constant polynomial in F, the ring of polynomials in the variable x with coefficients in F.

## Algorithm

In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.

## Almost all

In mathematics, the term "almost all" means "all but a negligible amount".

## Alternative algebra

In abstract algebra, an alternative algebra is an algebra in which multiplication need not be associative, only alternative.

## Ancient Egypt

Ancient Egypt was a civilization of ancient Northeastern Africa, concentrated along the lower reaches of the Nile River - geographically Lower Egypt and Upper Egypt, in the place that is now occupied by the countries of Egypt and Sudan.

## Ancient Greece

Ancient Greece was a civilization belonging to a period of Greek history from the Greek Dark Ages of the 13th–9th centuries BC to the end of antiquity (AD 600).

## Ancient Mesopotamian units of measurement

Ancient Mesopotamian units of measurement originated in the loosely organized city-states of Early Dynastic Sumer.

## Aristotle

Aristotle (Ἀριστοτέλης Aristotélēs,; 384–322 BC) was an ancient Greek philosopher and scientist born in the city of Stagira, Chalkidiki, in the north of Classical Greece.

## Arithmetic

Arithmetic (from the Greek ἀριθμός arithmos, "number") is a branch of mathematics that consists of the study of numbers, especially the properties of the traditional operations on them—addition, subtraction, multiplication and division.

## Arithmetica

Arithmetica (Ἀριθμητικά) is an Ancient Greek text on mathematics written by the mathematician Diophantus in the 3rd century AD.

## Associative property

In mathematics, the associative property is a property of some binary operations.

## August Ferdinand Möbius

August Ferdinand Möbius (17 November 1790 &ndash; 26 September 1868) was a German mathematician and theoretical astronomer.

## Augustin-Louis Cauchy

Baron Augustin-Louis Cauchy FRS FRSE (21 August 178923 May 1857) was a French mathematician, engineer and physicist who made pioneering contributions to several branches of mathematics, including: mathematical analysis and continuum mechanics.

## Évariste Galois

Évariste Galois (25 October 1811 – 31 May 1832) was a French mathematician.

## Bede

Bede (italic; 672/3 – 26 May 735), also known as Saint Bede, Venerable Bede, and Bede the Venerable (Bēda Venerābilis), was an English Benedictine monk at the monastery of St.

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## Bernhard Riemann

Georg Friedrich Bernhard Riemann (17 September 1826 – 20 July 1866) was a German mathematician who made contributions to analysis, number theory, and differential geometry.

## Bertrand Russell

Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 &ndash; 2 February 1970) was a British philosopher, logician, mathematician, historian, writer, social critic, political activist, and Nobel laureate.

## Bhāskara II

Bhāskara (also known as Bhāskarāchārya ("Bhāskara, the teacher"), and as Bhaskara II to avoid confusion with Bhāskara I) (1114–1185), was an Indian mathematician and astronomer.

## Bijection

In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set.

## Binary relation

In mathematics, a binary relation on a set A is a set of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2.

## Blackboard bold

Blackboard bold is a typeface style that is often used for certain symbols in mathematical texts, in which certain lines of the symbol (usually vertical or near-vertical lines) are doubled.

Brady John Haran (born 18 June 1976) is an Australian-born British independent filmmaker and video journalist who is known for his educational videos and documentary films produced for BBC News and his YouTube channels, the most notable being Periodic Videos and Numberphile.

## Brahmagupta

Brahmagupta (born, died) was an Indian mathematician and astronomer.

## Brāhmasphuṭasiddhānta

The Brāhmasphuṭasiddhānta ("Correctly Established Doctrine of Brahma", abbreviated BSS) is the main work of Brahmagupta, written c. 628.

## Byzantine Empire

The Byzantine Empire, also referred to as the Eastern Roman Empire and Byzantium, was the continuation of the Roman Empire in its eastern provinces during Late Antiquity and the Middle Ages, when its capital city was Constantinople (modern-day Istanbul, which had been founded as Byzantium).

## Calculation

A calculation is a deliberate process that transforms one or more inputs into one or more results, with variable change.

## Calculus

Calculus (from Latin calculus, literally 'small pebble', used for counting and calculations, as on an abacus), is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.

## Cardinal number

In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality (size) of sets.

## Cardinality

In mathematics, the cardinality of a set is a measure of the "number of elements of the set".

## Carl Friedrich Gauss

Johann Carl Friedrich Gauss (Gauß; Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields, including algebra, analysis, astronomy, differential geometry, electrostatics, geodesy, geophysics, magnetic fields, matrix theory, mechanics, number theory, optics and statistics.

## Cartesian coordinate system

A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.

## Caspar Wessel

Caspar Wessel (June 8, 1745, Vestby – March 25, 1818, Copenhagen) was a Danish–Norwegian mathematician and cartographer.

## Charles Hermite

Prof Charles Hermite FRS FRSE MIAS (24 December 1822 – 14 January 1901) was a French mathematician who did research concerning number theory, quadratic forms, invariant theory, orthogonal polynomials, elliptic functions, and algebra.

## Charles Jean de la Vallée Poussin

Charles-Jean Étienne Gustave Nicolas Le Vieux, Baron de la Vallée Poussin (14 August 1866 – 2 March 1962) was a Belgian mathematician.

## Charles Méray

Hugues Charles Robert Méray (12 November 1835, Chalon-sur-Saône, Saône-et-Loire - 2 February 1911, Dijon) was a French mathematician.

## China

China, officially the People's Republic of China (PRC), is a unitary one-party sovereign state in East Asia and the world's most populous country, with a population of around /1e9 round 3 billion.

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## Circa

Circa, usually abbreviated c., ca. or ca (also circ. or cca.), means "approximately" in several European languages (and as a loanword in English), usually in reference to a date.

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## Circumference

In geometry, the circumference (from Latin circumferentia, meaning "carrying around") of a circle is the (linear) distance around it.

## Coefficient

In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series or any expression; it is usually a number, but may be any expression.

## Commutative property

In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.

## Complete metric space

In mathematical analysis, a metric space M is called complete (or a Cauchy space) if every Cauchy sequence of points in M has a limit that is also in M or, alternatively, if every Cauchy sequence in M converges in M. Intuitively, a space is complete if there are no "points missing" from it (inside or at the boundary).

## Completeness of the real numbers

Intuitively, completeness implies that there are not any “gaps” (in Dedekind's terminology) or “missing points” in the real number line.

## Complex analysis

Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers.

## Complex number

A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.

## Complex plane

In mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the perpendicular imaginary axis.

## Computus

Computus (Latin for "computation") is a calculation that determines the calendar date of Easter.

## Concrete number

A concrete number or numerus numeratus is a number associated with the things being counted, in contrast to an abstract number or numerus numerans which is a number as a single entity.

## Continued fraction

In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on.

## Continuum hypothesis

In mathematics, the continuum hypothesis (abbreviated CH) is a hypothesis about the possible sizes of infinite sets.

## Countable set

In mathematics, a countable set is a set with the same cardinality (number of elements) as some subset of the set of natural numbers.

## Counting

Counting is the action of finding the number of elements of a finite set of objects.

## Crelle's Journal

Crelle's Journal, or just Crelle, is the common name for a mathematics journal, the Journal für die reine und angewandte Mathematik (in English: Journal for Pure and Applied Mathematics).

## Cubic function

In algebra, a cubic function is a function of the form in which is nonzero.

## Cyclotomic field

In number theory, a cyclotomic field is a number field obtained by adjoining a complex primitive root of unity to, the field of rational numbers.

## De Moivre's formula

In mathematics, de Moivre's formula (also known as de Moivre's theorem and de Moivre's identity), named after Abraham de Moivre, states that for any complex number (and, in particular, for any real number) and integer it holds that where is the imaginary unit.

## Decimal

The decimal numeral system (also called base-ten positional numeral system, and occasionally called denary) is the standard system for denoting integer and non-integer numbers.

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## Decimal separator

A decimal separator is a symbol used to separate the integer part from the fractional part of a number written in decimal form.

## Dedekind cut

In mathematics, Dedekind cuts, named after German mathematician Richard Dedekind, are а method of construction of the real numbers from the rational numbers.

## Determinant

In linear algebra, the determinant is a value that can be computed from the elements of a square matrix.

## Diameter

In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle.

## Dimension

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.

## Dionysius Exiguus

Dionysius Exiguus (Latin for "Dionysius the Humble"; –) was a 6th-century monk born in Scythia Minor (probably modern Dobruja, in Romania and Bulgaria).

## Diophantus

Diophantus of Alexandria (Διόφαντος ὁ Ἀλεξανδρεύς; born probably sometime between AD 201 and 215; died around 84 years old, probably sometime between AD 285 and 299) was an Alexandrian Hellenistic mathematician, who was the author of a series of books called Arithmetica, many of which are now lost.

## Divisibility rule

A divisibility rule is a shorthand way of determining whether a given integer is divisible by a fixed divisor without performing the division, usually by examining its digits.

## Division (mathematics)

Division is one of the four basic operations of arithmetic, the others being addition, subtraction, and multiplication.

## Division by zero

In mathematics, division by zero is division where the divisor (denominator) is zero.

## Double-entry bookkeeping system

Double-entry bookkeeping, in accounting, is a system of bookkeeping so named because every entry to an account requires a corresponding and opposite entry to a different account.

## Dover Publications

Dover Publications, also known as Dover Books, is an American book publisher founded in 1941 by Hayward Cirker and his wife, Blanche.

## Easter

Easter,Traditional names for the feast in English are "Easter Day", as in the Book of Common Prayer, "Easter Sunday", used by James Ussher and Samuel Pepys and plain "Easter", as in books printed in,, also called Pascha (Greek, Latin) or Resurrection Sunday, is a festival and holiday celebrating the resurrection of Jesus from the dead, described in the New Testament as having occurred on the third day of his burial after his crucifixion by the Romans at Calvary 30 AD.

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## Eduard Heine

Heinrich Eduard Heine (16 March 1821, Berlin &ndash; October 1881, Halle) was a German mathematician.

## Egypt

Egypt (مِصر, مَصر, Khēmi), officially the Arab Republic of Egypt, is a transcontinental country spanning the northeast corner of Africa and southwest corner of Asia by a land bridge formed by the Sinai Peninsula.

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## Egyptian fraction

An Egyptian fraction is a finite sum of distinct unit fractions, such as That is, each fraction in the expression has a numerator equal to 1 and a denominator that is a positive integer, and all the denominators differ from each other.

## Empty set

In mathematics, and more specifically set theory, the empty set or null set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero.

## Eratosthenes

Eratosthenes of Cyrene (Ἐρατοσθένης ὁ Κυρηναῖος,; –) was a Greek mathematician, geographer, poet, astronomer, and music theorist.

## Ernst Kummer

Ernst Eduard Kummer (29 January 1810 – 14 May 1893) was a German mathematician.

## Euclid

Euclid (Εὐκλείδης Eukleidēs; fl. 300 BC), sometimes given the name Euclid of Alexandria to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the "founder of geometry" or the "father of geometry".

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## Euclid's Elements

The Elements (Στοιχεῖα Stoicheia) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC.

## Euclidean algorithm

. EXAMPLES CAN BE FOUND BELOW, E.G., IN THE "Matrix method" SECTION.

## Euclidean division

In arithmetic, Euclidean division is the process of division of two integers, which produces a quotient and a remainder smaller than the divisor.

## Euler's formula

Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function.

## Europe

Europe is a continent located entirely in the Northern Hemisphere and mostly in the Eastern Hemisphere.

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## Exponentiation

Exponentiation is a mathematical operation, written as, involving two numbers, the base and the exponent.

## Felix Klein

Christian Felix Klein (25 April 1849 – 22 June 1925) was a German mathematician and mathematics educator, known for his work with group theory, complex analysis, non-Euclidean geometry, and on the associations between geometry and group theory.

## Ferdinand von Lindemann

Carl Louis Ferdinand von Lindemann (April 12, 1852 &ndash; March 6, 1939) was a German mathematician, noted for his proof, published in 1882, that pi (pi) is a transcendental number, meaning it is not a root of any polynomial with rational coefficients.

## Fibonacci

Fibonacci (c. 1175 – c. 1250) was an Italian mathematician from the Republic of Pisa, considered to be "the most talented Western mathematician of the Middle Ages".

## Fibonacci number

In mathematics, the Fibonacci numbers are the numbers in the following integer sequence, called the Fibonacci sequence, and characterized by the fact that every number after the first two is the sum of the two preceding ones: Often, especially in modern usage, the sequence is extended by one more initial term: By definition, the first two numbers in the Fibonacci sequence are either 1 and 1, or 0 and 1, depending on the chosen starting point of the sequence, and each subsequent number is the sum of the previous two.

## Field (mathematics)

In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers.

## Field extension

In mathematics, and in particular, algebra, a field E is an extension field of a field F if E contains F and the operations of F are those of E restricted to F. Equivalently, F is a subfield of E. For example, under the usual notions of addition and multiplication, the complex numbers are an extension field of the real numbers; the real numbers are a subfield of the complex numbers.

## Finite field

In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements.

## First-order logic

First-order logic—also known as first-order predicate calculus and predicate logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science.

## Formal grammar

In formal language theory, a grammar (when the context is not given, often called a formal grammar for clarity) is a set of production rules for strings in a formal language.

## Fraction (mathematics)

A fraction (from Latin fractus, "broken") represents a part of a whole or, more generally, any number of equal parts.

## Fractional part

The fractional part or decimal part of a non‐negative real number x is the excess beyond that number's integer part.

## Frustum

In geometry, a frustum (plural: frusta or frustums) is the portion of a solid (normally a cone or pyramid) that lies between one or two parallel planes cutting it.

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## Fundamental theorem of algebra

The fundamental theorem of algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root.

## Fundamental theorem of arithmetic

In number theory, the fundamental theorem of arithmetic, also called the unique factorization theorem or the unique-prime-factorization theorem, states that every integer greater than 1 either is a prime number itself or can be represented as the product of prime numbers and that, moreover, this representation is unique, up to (except for) the order of the factors.

## Galileo Galilei

Galileo Galilei (15 February 1564Drake (1978, p. 1). The date of Galileo's birth is given according to the Julian calendar, which was then in force throughout Christendom. In 1582 it was replaced in Italy and several other Catholic countries with the Gregorian calendar. Unless otherwise indicated, dates in this article are given according to the Gregorian calendar. – 8 January 1642) was an Italian polymath.

## Galois theory

In the field of algebra within mathematics, Galois theory, provides a connection between field theory and group theory.

## Gaussian integer

In number theory, a Gaussian integer is a complex number whose real and imaginary parts are both integers.

## Georg Cantor

Georg Ferdinand Ludwig Philipp Cantor (– January 6, 1918) was a German mathematician.

## Georg Cantor's first set theory article

Georg Cantor's first set theory article was published in 1874 and contains the first theorems of transfinite set theory, which studies infinite sets and their properties.

## Gerolamo Cardano

Gerolamo (or Girolamo, or Geronimo) Cardano (Jérôme Cardan; Hieronymus Cardanus; 24 September 1501 – 21 September 1576) was an Italian polymath, whose interests and proficiencies ranged from being a mathematician, physician, biologist, physicist, chemist, astrologer, astronomer, philosopher, writer, and gambler.

## Glossary of arithmetic and diophantine geometry

This is a glossary of arithmetic and diophantine geometry in mathematics, areas growing out of the traditional study of Diophantine equations to encompass large parts of number theory and algebraic geometry.

## Glyph

In typography, a glyph is an elemental symbol within an agreed set of symbols, intended to represent a readable character for the purposes of writing.

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## Goldbach's conjecture

Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics.

## Gottfried Wilhelm Leibniz

Gottfried Wilhelm (von) Leibniz (or; Leibnitz; – 14 November 1716) was a German polymath and philosopher who occupies a prominent place in the history of mathematics and the history of philosophy.

## Gotthold Eisenstein

Ferdinand Gotthold Max Eisenstein (16 April 1823 – 11 October 1852) was a German mathematician.

## Greatest common divisor

In mathematics, the greatest common divisor (gcd) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers.

## Greece

No description.

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## Greek alphabet

The Greek alphabet has been used to write the Greek language since the late 9th or early 8th century BC.

## Greek mathematics

Greek mathematics refers to mathematics texts and advances written in Greek, developed from the 7th century BC to the 4th century AD around the shores of the Eastern Mediterranean.

## Greek numerals

Greek numerals, also known as Ionic, Ionian, Milesian, or Alexandrian numerals, are a system of writing numbers using the letters of the Greek alphabet.

## Gresham College

Gresham College is an institution of higher learning located at Barnard's Inn Hall off Holborn in Central London, England.

## Group theory

In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.

## Hero of Alexandria

Hero of Alexandria (ἭρωνGenitive: Ἥρωνος., Heron ho Alexandreus; also known as Heron of Alexandria; c. 10 AD – c. 70 AD) was a mathematician and engineer who was active in his native city of Alexandria, Roman Egypt.

## Hipparchus

Hipparchus of Nicaea (Ἵππαρχος, Hipparkhos) was a Greek astronomer, geographer, and mathematician.

## Hippasus

Hippasus of Metapontum (Ἵππασος ὁ Μεταποντῖνος, Híppasos; fl. 5th century BC), was a Pythagorean philosopher.

## Hypercomplex number

In mathematics, a hypercomplex number is a traditional term for an element of a unital algebra over the field of real numbers.

## Hyperreal number

The system of hyperreal numbers is a way of treating infinite and infinitesimal quantities.

## Ideal number

In number theory an ideal number is an algebraic integer which represents an ideal in the ring of integers of a number field; the idea was developed by Ernst Kummer, and led to Richard Dedekind's definition of ideals for rings.

## Imaginary number

An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit,j is usually used in Engineering contexts where i has other meanings (such as electrical current) which is defined by its property.

## Imaginary unit

The imaginary unit or unit imaginary number is a solution to the quadratic equation.

## India

India (IAST), also called the Republic of India (IAST), is a country in South Asia.

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## Indian mathematics

Indian mathematics emerged in the Indian subcontinent from 1200 BC until the end of the 18th century.

## Infimum and supremum

In mathematics, the infimum (abbreviated inf; plural infima) of a subset S of a partially ordered set T is the greatest element in T that is less than or equal to all elements of S, if such an element exists.

## Infinitesimal

In mathematics, infinitesimals are things so small that there is no way to measure them.

## Infinity

Infinity (symbol) is a concept describing something without any bound or larger than any natural number.

## Integer

An integer (from the Latin ''integer'' meaning "whole")Integer&#x2009;'s first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").

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## Integer sequence

In mathematics, an integer sequence is a sequence (i.e., an ordered list) of integers.

## International Standard Book Number

The International Standard Book Number (ISBN) is a unique numeric commercial book identifier.

## Irrational number

In mathematics, the irrational numbers are all the real numbers which are not rational numbers, the latter being the numbers constructed from ratios (or fractions) of integers.

## Isaac Newton

Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, astronomer, theologian, author and physicist (described in his own day as a "natural philosopher") who is widely recognised as one of the most influential scientists of all time, and a key figure in the scientific revolution.

## Isomorphism

In mathematics, an isomorphism (from the Ancient Greek: ἴσος isos "equal", and μορφή morphe "form" or "shape") is a homomorphism or morphism (i.e. a mathematical mapping) that can be reversed by an inverse morphism.

Jacques Salomon Hadamard ForMemRS (8 December 1865 – 17 October 1963) was a French mathematician who made major contributions in number theory, complex function theory, differential geometry and partial differential equations.

## Jainism

Jainism, traditionally known as Jain Dharma, is an ancient Indian religion.

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## John Wallis

John Wallis (3 December 1616 – 8 November 1703) was an English clergyman and mathematician who is given partial credit for the development of infinitesimal calculus.

## Joseph Liouville

Joseph Liouville FRS FRSE FAS (24 March 1809 – 8 September 1882) was a French mathematician.

## Joseph-Louis Lagrange

Joseph-Louis Lagrange (or;; born Giuseppe Lodovico Lagrangia, Encyclopædia Britannica or Giuseppe Ludovico De la Grange Tournier, Turin, 25 January 1736 – Paris, 10 April 1813; also reported as Giuseppe Luigi Lagrange or Lagrangia) was an Italian Enlightenment Era mathematician and astronomer.

## Kahun Papyri

The Kahun Papyri (KP) (also Petrie Papyri or Lahun Papyri) are a collection of ancient Egyptian texts discussing administrative, mathematical and medical topics.

## Karl Weierstrass

Karl Theodor Wilhelm Weierstrass (Weierstraß; 31 October 1815 – 19 February 1897) was a German mathematician often cited as the "father of modern analysis".

## Khmer numerals

Khmer numerals are the numerals used in the Khmer language.

## Leonhard Euler

Leonhard Euler (Swiss Standard German:; German Standard German:; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer, who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory.

## Leopold Kronecker

Leopold Kronecker (7 December 1823 – 29 December 1891) was a German mathematician who worked on number theory, algebra and logic.

## Liber Abaci

Liber Abaci (1202, also spelled as Liber Abbaci) is a historic book on arithmetic by Leonardo of Pisa, known later by his nickname Fibonacci.

## List of mathematical symbols

This is a list of symbols used in all branches of mathematics to express a formula or to represent a constant.

## List of numbers in various languages

The following tables list the cardinal number names and symbols for the numbers 0 through 10 in various languages and scripts of the world.

## Margin of error

The margin of error is a statistic expressing the amount of random sampling error in a survey's results.

## Mathematical constant

A mathematical constant is a special number that is "significantly interesting in some way".

## Mathematical object

A mathematical object is an abstract object arising in mathematics.

## Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

## Maya calendar

The Maya calendar is a system of calendars used in pre-Columbian Mesoamerica and in many modern communities in the Guatemalan highlands, Veracruz, Oaxaca and Chiapas, Mexico.

## Maya numerals

The Mayan numeral system was the system to represent numbers and calendar dates in the Maya civilization.

## Measurement

Measurement is the assignment of a number to a characteristic of an object or event, which can be compared with other objects or events.

## Merriam-Webster

Merriam–Webster, Incorporated is an American company that publishes reference books which is especially known for its dictionaries.

## Mexico

Mexico (México; Mēxihco), officially called the United Mexican States (Estados Unidos Mexicanos) is a federal republic in the southern portion of North America.

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## Monic polynomial

In algebra, a monic polynomial is a single-variable polynomial (that is, a univariate polynomial) in which the leading coefficient (the nonzero coefficient of highest degree) is equal to 1.

## Morris Kline

Morris Kline (May 1, 1908 – June 10, 1992) was a Professor of Mathematics, a writer on the history, philosophy, and teaching of mathematics, and also a popularizer of mathematical subjects.

## Multiplication

Multiplication (often denoted by the cross symbol "×", by a point "⋅", by juxtaposition, or, on computers, by an asterisk "∗") is one of the four elementary mathematical operations of arithmetic; with the others being addition, subtraction and division.

## Muslim world

The terms Muslim world and Islamic world commonly refer to the unified Islamic community (Ummah), consisting of all those who adhere to the religion of Islam, or to societies where Islam is practiced.

## Mythical number

Not to be confused with an imaginary number.

## Natural number

In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").

## Negative number

In mathematics, a negative number is a real number that is less than zero.

## Niccolò Fontana Tartaglia

Niccolò Fontana Tartaglia (1499/1500, Brescia &ndash; 13 December 1557, Venice) was a Venetian mathematician, engineer (designing fortifications), a surveyor (of topography, seeking the best means of defense or offense) and a bookkeeper from the then-Republic of Venice (now part of Italy).

## Nicolas Chuquet

Nicolas Chuquet (1445, but some sources say 1455, Paris, France &ndash; 1488, some sources say 1500, Lyon, France) was a French mathematician.

## Niels Henrik Abel

Niels Henrik Abel (5 August 1802 – 6 April 1829) was a Norwegian mathematician who made pioneering contributions in a variety of fields.

## Nominal number

Nominal numbers or categorical numbers are numeric codes, meaning numerals used for labelling or identification only.

## Non-standard analysis

The history of calculus is fraught with philosophical debates about the meaning and logical validity of fluxions or infinitesimal numbers.

## Nth root

In mathematics, an nth root of a number x, where n is usually assumed to be a positive integer, is a number r which, when raised to the power n yields x: where n is the degree of the root.

## Number line

In basic mathematics, a number line is a picture of a graduated straight line that serves as abstraction for real numbers, denoted by \mathbb.

## Number theory

Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers.

## Numeral (linguistics)

In linguistics, a numeral is a member of a part of speech characterized by the designation of numbers; some examples are the English word 'two' and the compound 'seventy-seventh'.

## Numeral system

A numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner.

## Numerical cognition

Numerical cognition is a subdiscipline of cognitive science that studies the cognitive, developmental and neural bases of numbers and mathematics.

## Numerical digit

A numerical digit is a single symbol (such as "2" or "5") used alone, or in combinations (such as "25"), to represent numbers (such as the number 25) according to some positional numeral systems.

## Numerology

Numerology is any belief in the divine or mystical relationship between a number and one or more coinciding events.

## Octonion

In mathematics, the octonions are a normed division algebra over the real numbers, usually represented by the capital letter O, using boldface O or blackboard bold \mathbb O. There are three lower-dimensional normed division algebras over the reals: the real numbers R themselves, the complex numbers C, and the quaternions H. The octonions have eight dimensions; twice the number of dimensions of the quaternions, of which they are an extension.

## Olmecs

The Olmecs were the earliest known major civilization in Mexico following a progressive development in Soconusco.

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## Omicron

Omicron (uppercase Ο, lowercase ο, literally "small o": όμικρον back rounded vowel. Letters that arose from omicron include Roman O and Cyrillic O. The upper-case letter of omicron (O) was originally used in mathematics as a symbol for Big O notation (representing a function's asymptotic growth rate), but has fallen out of favor because omicron is indistinguishable from the Latin letter O and easily confused with the digit zero (0). Omicron is used to designate the fifteenth star in a constellation group, its ordinal placement a function of both magnitude and position. Such stars include Omicron Andromedae, Omicron Ceti, and Omicron Persei.

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## One half

One half is the irreducible fraction resulting from dividing one by two or the fraction resulting from dividing any number by its double.

## Order of magnitude

An order of magnitude is an approximate measure of the number of digits that a number has in the commonly-used base-ten number system.

## Ordered field

In mathematics, an ordered field is a field together with a total ordering of its elements that is compatible with the field operations.

## Ordinal number

In set theory, an ordinal number, or ordinal, is one generalization of the concept of a natural number that is used to describe a way to arrange a collection of objects in order, one after another.

## Paolo Ruffini

Paolo Ruffini (September 22, 1765 – May 10, 1822) was an Italian mathematician and philosopher.

## Paul Halmos

Paul Richard Halmos (Halmos Pál; March 3, 1916 – October 2, 2006) was a Hungarian-Jewish-born American mathematician who made fundamental advances in the areas of mathematical logic, probability theory, statistics, operator theory, ergodic theory, and functional analysis (in particular, Hilbert spaces).

## Paul Tannery

Paul Tannery (20 December 1843 – 27 November 1904) was a French mathematician and historian of mathematics.

## Pāṇini

(पाणिनि, Frits Staal (1965),, Philosophy East and West, Vol. 15, No. 2 (Apr., 1965), pp. 99-116) is an ancient Sanskrit philologist, grammarian, and a revered scholar in Hinduism.

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## Peano axioms

In mathematical logic, the Peano axioms, also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers presented by the 19th century Italian mathematician Giuseppe Peano.

## Perfect number

In number theory, a perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself (also known as its aliquot sum).

## Perspective (graphical)

Perspective (from perspicere "to see through") in the graphic arts is an approximate representation, generally on a flat surface (such as paper), of an image as it is seen by the eye.

## Philosophy

Philosophy (from Greek φιλοσοφία, philosophia, literally "love of wisdom") is the study of general and fundamental problems concerning matters such as existence, knowledge, values, reason, mind, and language.

## Physical constant

A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity that is generally believed to be both universal in nature and have constant value in time.

## Pi

The number is a mathematical constant.

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## Pingala

Pingala (Devanagari: पिङ्गल) (c. 3rd/2nd century BC) was an ancient Indian mathematician who authored the (also called Pingala-sutras), the earliest known treatise on Sanskrit prosody.

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## Plus and minus signs

The plus and minus signs (+ and −) are mathematical symbols used to represent the notions of positive and negative as well as the operations of addition and subtraction.

## Polynomial

In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

## Positional notation

Positional notation or place-value notation is a method of representing or encoding numbers.

## Prehistory

Human prehistory is the period between the use of the first stone tools 3.3 million years ago by hominins and the invention of writing systems.

## Prime number

A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.

## Prime number theorem

In number theory, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers among the positive integers.

## Principia Mathematica

The Principia Mathematica (often abbreviated PM) is a three-volume work on the foundations of mathematics written by Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913.

## Projective geometry

Projective geometry is a topic in mathematics.

## Proof that π is irrational

In the 18th century, Johann Heinrich Lambert proved that the number pi (pi) is irrational: that is, it cannot be expressed as a fraction a/b, where a is an integer and b is a non-zero integer.

## Pseudoscience

Pseudoscience consists of statements, beliefs, or practices that are claimed to be both scientific and factual, but are incompatible with the scientific method.

## Ptolemy

Claudius Ptolemy (Κλαύδιος Πτολεμαῖος, Klaúdios Ptolemaîos; Claudius Ptolemaeus) was a Greco-Roman mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology.

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## Pyramid

A pyramid (from πυραμίς) is a structure whose outer surfaces are triangular and converge to a single point at the top, making the shape roughly a pyramid in the geometric sense.

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## Pythagoras

Pythagoras of Samos was an Ionian Greek philosopher and the eponymous founder of the Pythagoreanism movement.

## Pythagoreanism

Pythagoreanism originated in the 6th century BC, based on the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans, who were considerably influenced by mathematics and mysticism.

In elementary algebra, the quadratic formula is the solution of the quadratic equation.

In algebra, a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic, is a polynomial function in one or more variables in which the highest-degree term is of the second degree.

## Quaternion

In mathematics, the quaternions are a number system that extends the complex numbers.

## Quintic function

In algebra, a quintic function is a function of the form where,,,, and are members of a field, typically the rational numbers, the real numbers or the complex numbers, and is nonzero.

## Quotient

In arithmetic, a quotient (from quotiens "how many times", pronounced) is the quantity produced by the division of two numbers.

In mathematical numeral systems, the radix or base is the number of unique digits, including zero, used to represent numbers in a positional numeral system.

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## Rational number

In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.

## Real closed field

In mathematics, a real closed field is a field F that has the same first-order properties as the field of real numbers.

## Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

## Rectangle

In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles.

## Renaissance

The Renaissance is a period in European history, covering the span between the 14th and 17th centuries.

## René Descartes

René Descartes (Latinized: Renatus Cartesius; adjectival form: "Cartesian"; 31 March 1596 – 11 February 1650) was a French philosopher, mathematician, and scientist.

## Repeating decimal

A repeating or recurring decimal is decimal representation of a number whose digits are periodic (repeating its values at regular intervals) and the infinitely-repeated portion is not zero.

## Rhind Mathematical Papyrus

The Rhind Mathematical Papyrus (RMP; also designated as papyrus British Museum 10057 and pBM 10058) is one of the best known examples of Egyptian mathematics.

## Richard Dedekind

Julius Wilhelm Richard Dedekind (6 October 1831 – 12 February 1916) was a German mathematician who made important contributions to abstract algebra (particularly ring theory), axiomatic foundation for the natural numbers, algebraic number theory and the definition of the real numbers.

## Riemann hypothesis

In mathematics, the Riemann hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part.

## Riemann sphere

In mathematics, the Riemann sphere, named after Bernhard Riemann, is a model of the extended complex plane, the complex plane plus a point at infinity.

## Ring (mathematics)

In mathematics, a ring is one of the fundamental algebraic structures used in abstract algebra.

## Root of unity

In mathematics, a root of unity, occasionally called a de Moivre number, is any complex number that gives 1 when raised to some positive integer power.

## Rounding

Rounding a numerical value means replacing it by another value that is approximately equal but has a shorter, simpler, or more explicit representation; for example, replacing \$ with \$, or the fraction 312/937 with 1/3, or the expression with.

## Salvatore Pincherle

Salvatore Pincherle (March 11, 1853 &ndash; July 10, 1936) was an Italian mathematician.

## Sanskrit

Sanskrit is the primary liturgical language of Hinduism; a philosophical language of Hinduism, Sikhism, Buddhism and Jainism; and a former literary language and lingua franca for the educated of ancient and medieval India.

## Sedenion

In abstract algebra, the sedenions form a 16-dimensional noncommutative and nonassociative algebra over the reals obtained by applying the Cayley–Dickson construction to the octonions.

## Serial code

A serial code is a unique identifier assigned incrementally or sequentially to an item.

## Set (mathematics)

In mathematics, a set is a collection of distinct objects, considered as an object in its own right.

## Set theory

Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.

## Shulba Sutras

The Shulba Sutras or Śulbasūtras (Sanskrit: "string, cord, rope") are sutra texts belonging to the Śrauta ritual and containing geometry related to fire-altar construction.

## Sieve of Eratosthenes

In mathematics, the sieve of Eratosthenes is a simple, ancient algorithm for finding all prime numbers up to any given limit.

## Significant figures

The significant figures (also known as the significant digits) of a number are digits that carry meaning contributing to its measurement resolution.

## Singularity (mathematics)

In mathematics, a singularity is in general a point at which a given mathematical object is not defined, or a point of an exceptional set where it fails to be well-behaved in some particular way, such as differentiability.

Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.

## Square root

In mathematics, a square root of a number a is a number y such that; in other words, a number y whose square (the result of multiplying the number by itself, or) is a. For example, 4 and −4 are square roots of 16 because.

## Square root of 2

The square root of 2, or the (1/2)th power of 2, written in mathematics as or, is the positive algebraic number that, when multiplied by itself, gives the number 2.

## Sthananga Sutra

Sthananga Sutra (Sanskrit: Sthānāṅgasūtra Prakrit: Ṭhāṇaṃgasutta) (c. 3rd-4th century CE) forms part of the first eleven Angas of the Jaina Canon which have survived despite the bad effects of this Hundavasarpini kala as per the Śvetāmbara belief.

## Subitizing

Subitizing is the rapid, accurate, and confident judgments of numbers performed for small numbers of items.

## Subset

In mathematics, a set A is a subset of a set B, or equivalently B is a superset of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide.

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## Subtraction

Subtraction is an arithmetic operation that represents the operation of removing objects from a collection.

## Superreal number

In abstract algebra, the superreal numbers are a class of extensions of the real numbers, introduced by H. Garth Dales and W. Hugh Woodin as a generalization of the hyperreal numbers and primarily of interest in non-standard analysis, model theory, and the study of Banach algebras.

## Surreal number

In mathematics, the surreal number system is a totally ordered proper class containing the real numbers as well as infinite and infinitesimal numbers, respectively larger or smaller in absolute value than any positive real number.

## Symbol

A symbol is a mark, sign or word that indicates, signifies, or is understood as representing an idea, object, or relationship.

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## Tally marks

Tally marks, also called hash marks, are a unary numeral system.

## Telephone number

A telephone number is a sequence of digits assigned to a fixed-line telephone subscriber station connected to a telephone line or to a wireless electronic telephony device, such as a radio telephone or a mobile telephone, or to other devices for data transmission via the public switched telephone network (PSTN) or other private networks.

## The Nine Chapters on the Mathematical Art

The Nine Chapters on the Mathematical Art is a Chinese mathematics book, composed by several generations of scholars from the 10th&ndash;2nd century BCE, its latest stage being from the 2nd century CE.

## The Princeton Companion to Mathematics

The Princeton Companion to Mathematics is a book, edited by Timothy Gowers with associate editors June Barrow-Green and Imre Leader, and published in 2008 by Princeton University Press.

## Tobias Dantzig

Tobias Dantzig (February 19, 1884 – August 9, 1956) was a mathematician of Baltic German and Russian American heritage, the father of George Dantzig, and the author of Number: The Language of Science (A critical survey written for the cultured non-mathematician) (1930) and Aspects of Science (New York, Macmillan, 1937).

## Total order

In mathematics, a linear order, total order, simple order, or (non-strict) ordering is a binary relation on some set X, which is antisymmetric, transitive, and a connex relation.

## Transcendental number

In mathematics, a transcendental number is a real or complex number that is not algebraic—that is, it is not a root of a nonzero polynomial equation with integer (or, equivalently, rational) coefficients.

## Transfer principle

In model theory, a transfer principle states that all statements of some language that are true for some structure are true for another structure.

## Transfinite number

Transfinite numbers are numbers that are "infinite" in the sense that they are larger than all finite numbers, yet not necessarily absolutely infinite.

## Truncation

In mathematics and computer science, truncation is limiting the number of digits right of the decimal point.

## Turing machine

A Turing machine is a mathematical model of computation that defines an abstract machine, which manipulates symbols on a strip of tape according to a table of rules.

## Two New Sciences

The Discourses and Mathematical Demonstrations Relating to Two New Sciences (Discorsi e Dimostrazioni Matematiche Intorno a Due Nuove Scienze), published in 1638 was Galileo's final book and a scientific testament covering much of his work in physics over the preceding thirty years.

## Uncountable set

In mathematics, an uncountable set (or uncountably infinite set) is an infinite set that contains too many elements to be countable.

## Vacuum

Vacuum is space devoid of matter.

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## Vector space

A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.

## Victor Puiseux

Victor Alexandre Puiseux (16 April 1820 &ndash; 9 September 1883) was a French mathematician and astronomer.

## William Rowan Hamilton

Sir William Rowan Hamilton MRIA (4 August 1805 – 2 September 1865) was an Irish mathematician who made important contributions to classical mechanics, optics, and algebra.

## Yajurveda

The Yajurveda (Sanskrit: यजुर्वेद,, from meaning "prose mantra" and veda meaning "knowledge") is the Veda of prose mantras.

## Zeno of Elea

Zeno of Elea (Ζήνων ὁ Ἐλεάτης) was a pre-Socratic Greek philosopher of Magna Graecia and a member of the Eleatic School founded by Parmenides.

Zeno's paradoxes are a set of philosophical problems generally thought to have been devised by Greek philosopher Zeno of Elea (c. 490–430 BC) to support Parmenides' doctrine that contrary to the evidence of one's senses, the belief in plurality and change is mistaken, and in particular that motion is nothing but an illusion.

## Zero of a function

In mathematics, a zero, also sometimes called a root, of a real-, complex- or generally vector-valued function f is a member x of the domain of f such that f(x) vanishes at x; that is, x is a solution of the equation f(x).

## 0

0 (zero) is both a number and the numerical digit used to represent that number in numerals.

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## 0.999...

In mathematics, 0.999... (also written 0., among other ways), denotes the repeating decimal consisting of infinitely many 9s after the decimal point (and one 0 before it).

## 1

1 (one, also called unit, unity, and (multiplicative) identity) is a number, numeral, and glyph.

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## 1,000,000

1,000,000 (one million), or one thousand thousand, is the natural number following 999,999 and preceding 1,000,001.

## 13 (number)

13 (thirteen) is the natural number following 12 and preceding 14.

## 2

2 (two) is a number, numeral, and glyph.

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## 3

3 (three) is a number, numeral, and glyph.

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## 4

4 (four) is a number, numeral, and glyph.

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## References

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