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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]

156 relations: A. H. Lightstone, Algebraic structure, Almost all, American Mathematical Monthly, April Fools' Day, Archimedean property, Axiom, Ayn Rand, Balanced ternary, Base (exponentiation), Battle.net, Bijection, Binary number, Birmingham, Blizzard Entertainment, Cancellation property, Cantor set, Cantor's diagonal argument, Cauchy sequence, Chicago Reader, Combinatorial game theory, Commutative property, Completeness (order theory), Complex analysis, Construction of the real numbers, Continuous function, Convergent series, Counterexample, Counterintuitive, Cut-the-Knot, Data compression, David Tall, Decimal, Decimal separator, Dedekind cut, Dense set, Disjoint sets, Division by zero, Eduard Heine, Educational Studies in Mathematics, Elementary proof, Elements of Algebra, Elwyn Berlekamp, Equivalence relation, Factorial number system, FAQ, Fermat number, Field (mathematics), Finite set, Finitism, ... Expand index (106 more) »

## A. H. Lightstone

Albert Harold Lightstone (1926–1976) was a Canadian mathematician.

## Algebraic structure

In mathematics, and more specifically in abstract algebra, an algebraic structure on a set A (called carrier set or underlying set) is a collection of finitary operations on A; the set A with this structure is also called an algebra.

## Almost all

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

## American Mathematical Monthly

The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894.

## April Fools' Day

April Fools' Day is an annual celebration in some European and Western countries commemorated on April 1 by playing practical jokes and spreading hoaxes.

## Archimedean property

In abstract algebra and analysis, the Archimedean property, named after the ancient Greek mathematician Archimedes of Syracuse, is a property held by some algebraic structures, such as ordered or normed groups, and fields.

## Axiom

An axiom or postulate is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments.

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## Ayn Rand

Ayn Rand (born Alisa Zinovyevna Rosenbaum; – March 6, 1982) was a Russian-American writer and philosopher.

## Balanced ternary

Balanced ternary is a non-standard positional numeral system (a balanced form), used in some early computers and useful in the solution of balance puzzles.

## Base (exponentiation)

In exponentiation, the base is the number b in an expression of the form bn.

## Battle.net

Blizzard Battle.net is an Internet-based online gaming, social networking, digital distribution, and digital rights management platform developed by Blizzard Entertainment.

## 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 number

In mathematics and digital electronics, a binary number is a number expressed in the base-2 numeral system or binary numeral system, which uses only two symbols: typically 0 (zero) and 1 (one).

## Birmingham

Birmingham is a city and metropolitan borough in the West Midlands, England, with an estimated population of 1,101,360, making it the second most populous city of England and the United Kingdom.

## Blizzard Entertainment

Blizzard Entertainment, Inc. is an American video game developer and publisher based in Irvine, California, and is a subsidiary of the American company Activision Blizzard.

## Cancellation property

In mathematics, the notion of cancellative is a generalization of the notion of invertible.

## Cantor set

In mathematics, the Cantor set is a set of points lying on a single line segment that has a number of remarkable and deep properties.

## Cantor's diagonal argument

In set theory, Cantor's diagonal argument, also called the diagonalisation argument, the diagonal slash argument or the diagonal method, was published in 1891 by Georg Cantor as a mathematical proof that there are infinite sets which cannot be put into one-to-one correspondence with the infinite set of natural numbers.

## Cauchy sequence

In mathematics, a Cauchy sequence, named after Augustin-Louis Cauchy, is a sequence whose elements become arbitrarily close to each other as the sequence progresses.

The Chicago Reader, or Reader (stylized as ЯEADER), is an American alternative weekly newspaper in Chicago, Illinois, noted for its literary style of journalism and coverage of the arts, particularly film and theater.

## Combinatorial game theory

Combinatorial game theory (CGT) is a branch of mathematics and theoretical computer science that typically studies sequential games with perfect information.

## Commutative property

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

## Completeness (order theory)

In the mathematical area of order theory, completeness properties assert the existence of certain infima or suprema of a given partially ordered set (poset).

## 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.

## Construction of the real numbers

In mathematics, there are several ways of defining the real number system as an ordered field.

## Continuous function

In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.

## Convergent series

In mathematics, a series is the sum of the terms of an infinite sequence of numbers.

## Counterexample

In logic, and especially in its applications to mathematics and philosophy, a counterexample is an exception to a proposed general rule or law.

## Counterintuitive

A counterintuitive proposition is one that does not seem likely to be true when assessed using intuition, common sense, or gut feelings.

## Cut-the-Knot

Cut-the-knot is a free, advertisement-funded educational website maintained by Alexander Bogomolny and devoted to popular exposition of many topics in mathematics.

## Data compression

In signal processing, data compression, source coding, or bit-rate reduction involves encoding information using fewer bits than the original representation.

## David Tall

David Orme Tall (born 15 May 1941) is Emeritus Professor in Mathematical Thinking at the University of Warwick.

## 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.

## 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.

## Dense set

In topology and related areas of mathematics, a subset A of a topological space X is called dense (in X) if every point x in X either belongs to A or is a limit point of A, that is the closure of A is constituting the whole set X. Informally, for every point in X, the point is either in A or arbitrarily "close" to a member of A &mdash; for instance, every real number either is a rational number or has a rational number arbitrarily close to it (see Diophantine approximation).

## Disjoint sets

In mathematics, two sets are said to be disjoint sets if they have no element in common.

## Division by zero

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

## Eduard Heine

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

## Educational Studies in Mathematics

Educational Studies in Mathematics is a peer-reviewed scientific journal within the field of mathematics education.

## Elementary proof

In mathematics, an elementary proof is a mathematical proof that only uses basic techniques.

## Elements of Algebra

Elements of Algebra is an elementary mathematics textbook written by mathematician Leonhard Euler and originally published in 1770 in German.

## Elwyn Berlekamp

Elwyn Ralph Berlekamp (born September 6, 1940) is an American mathematician.

## Equivalence relation

In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive.

## Factorial number system

In combinatorics, the factorial number system, also called factoradic, is a mixed radix numeral system adapted to numbering permutations.

## FAQ

Frequently asked questions (FAQ) or Questions and Answers (Q&A), are listed questions and answers, all supposed to be commonly asked in some context, and pertaining to a particular topic.

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## Fermat number

In mathematics a Fermat number, named after Pierre de Fermat who first studied them, is a positive integer of the form where n is a nonnegative integer.

## 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.

## Finite set

In mathematics, a finite set is a set that has a finite number of elements.

## Finitism

Finitism is a philosophy of mathematics that accepts the existence only of finite mathematical objects.

## Fractal

In mathematics, a fractal is an abstract object used to describe and simulate naturally occurring objects.

## Fractional part

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

## General topology

In mathematics, general topology is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology.

## Geometric series

In mathematics, a geometric series is a series with a constant ratio between successive terms.

## Georg Cantor

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

## Golden ratio base

Golden ratio base is a non-integer positional numeral system that uses the golden ratio (the irrational number ≈ 1.61803399 symbolized by the Greek letter φ) as its base.

## Grammar school

A grammar school is one of several different types of school in the history of education in the United Kingdom and other English-speaking countries, originally a school teaching Latin, but more recently an academically-oriented secondary school, differentiated in recent years from less academic Secondary Modern Schools.

## 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.

## Group (mathematics)

In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.

## Hackenbush

Hackenbush is a two-player game invented by mathematician John Horton Conway.

## Heuristic

A heuristic technique (εὑρίσκω, "find" or "discover"), often called simply a heuristic, is any approach to problem solving, learning, or discovery that employs a practical method, not guaranteed to be optimal, perfect, logical, or rational, but instead sufficient for reaching an immediate goal.

## Hyperinteger

In non-standard analysis, a hyperinteger n is a hyperreal number that is equal to its own integer part.

## Hyperreal number

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

## Ian Stewart (mathematician)

Ian Nicholas Stewart (born 24 September 1945) is a British mathematician and a popular-science and science-fiction writer.

## Ideal theory

In mathematics, ideal theory is the theory of ideals in commutative rings; and is the precursor name for the contemporary subject of commutative algebra.

## IEEE 754

The IEEE Standard for Floating-Point Arithmetic (IEEE 754) is a technical standard for floating-point computation established in 1985 by the Institute of Electrical and Electronics Engineers (IEEE).

## 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.

## Infinite set

In set theory, an infinite set is a set that is not a finite set.

## 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.

## Informal mathematics

Informal mathematics, also called naïve mathematics, has historically been the predominant form of mathematics at most times and in most cultures, and is the subject of modern ethno-cultural studies of mathematics.

## 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").

## Internet

The Internet is the global system of interconnected computer networks that use the Internet protocol suite (TCP/IP) to link devices worldwide.

## Internet forum

An Internet forum, or message board, is an online discussion site where people can hold conversations in the form of posted messages.

## Intersection (set theory)

In mathematics, the intersection A ∩ B of two sets A and B is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements.

## Interval (mathematics)

In mathematics, a (real) interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set.

## Intuitionism

In the philosophy of mathematics, intuitionism, or neointuitionism (opposed to preintuitionism), is an approach where mathematics is considered to be purely the result of the constructive mental activity of humans rather than the discovery of fundamental principles claimed to exist in an objective reality.

## Joseph Mazur

Joseph C. Mazur (born in the Bronx in 1942) is Professor Emeritus of Mathematics at Marlboro College, in Marlboro, Vermont.

## Komornik–Loreti constant

The Komornik–Loreti constant is a mathematical constant that represents the smallest number for which there still exists a unique q-development.

## 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.

## Lexicographical order

In mathematics, the lexicographic or lexicographical order (also known as lexical order, dictionary order, alphabetical order or lexicographic(al) product) is a generalization of the way words are alphabetically ordered based on the alphabetical order of their component letters.

## Lightbulb joke

A lightbulb joke is a joke that asks how many people of a certain group are needed to change, replace, or screw in a light bulb.

## Limit (mathematics)

In mathematics, a limit is the value that a function (or sequence) "approaches" as the input (or index) "approaches" some value.

## Limit of a sequence

As the positive integer n becomes larger and larger, the value n\cdot \sin\bigg(\frac1\bigg) becomes arbitrarily close to 1.

## Mathematical Association of America

The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level.

## Mathematical joke

A mathematical joke is a form of humor which relies on aspects of mathematics or a stereotype of mathematicians to derive humor.

## Mathematical proof

In mathematics, a proof is an inferential argument for a mathematical statement.

## Mathematics

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

## Mathematics education

In contemporary education, mathematics education is the practice of teaching and learning mathematics, along with the associated scholarly research.

## Mathematics Magazine

Mathematics Magazine is a refereed bimonthly publication of the Mathematical Association of America.

## Metamath

Metamath is a language for developing strictly formalized mathematical definitions and proofs accompanied by a proof checker for this language and a growing database of thousands of proved theorems covering conventional results in logic, set theory, number theory, group theory, algebra, analysis, and topology, as well as topics in Hilbert spaces and quantum logic.

## Microsoft Developer Network

Microsoft Developer Network (MSDN) is the portion of Microsoft responsible for managing the firm's relationship with developers and testers, such as hardware developers interested in the operating system (OS), and software developers developing on the various OS platforms or using the API or scripting languages of Microsoft's applications.

## Midy's theorem

In mathematics, Midy's theorem, named after French mathematician E. Midy, is a statement about the decimal expansion of fractions a/p where p is a prime and a/p has a repeating decimal expansion with an even period.

Mixed radix numeral systems are non-standard positional numeral systems in which the numerical base varies from position to position.

## Modular arithmetic

In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus (plural moduli).

## Monoid

In abstract algebra, a branch of mathematics, a monoid is an algebraic structure with a single associative binary operation and an identity element.

## Monotonic function

In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order.

## 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").

## Nested intervals

In mathematics, a sequence of nested intervals is understood as a collection of sets of real numbers such that each set is an interval of the real line, for n.

## Non-standard analysis

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

## Non-standard positional numeral systems

Non-standard positional numeral systems here designates numeral systems that may loosely be described as positional systems, but that do not entirely comply with the following description of standard positional systems: This article summarizes facts on some non-standard positional numeral systems.

## Notices of the American Mathematical Society

Notices of the American Mathematical Society is the membership journal of the American Mathematical Society (AMS), published monthly except for the combined June/July issue.

## Number

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

## 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.

## Ones' complement

The ones' complement of a binary number is defined as the value obtained by inverting all the bits in the binary representation of the number (swapping 0s for 1s and vice versa).

## Order (group theory)

In group theory, a branch of mathematics, the term order is used in two unrelated senses.

## Order theory

Order theory is a branch of mathematics which investigates the intuitive notion of order using binary relations.

## 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.

In mathematics, the -adic number system for any prime number extends the ordinary arithmetic of the rational numbers in a different way from the extension of the rational number system to the real and complex number systems.

A paradox is a statement that, despite apparently sound reasoning from true premises, leads to an apparently self-contradictory or logically unacceptable conclusion.

## Partition of a set

In mathematics, a partition of a set is a grouping of the set's elements into non-empty subsets, in such a way that every element is included in one and only one of the subsets.

## Paul Erdős

Paul Erdős (Erdős Pál; 26 March 1913 – 20 September 1996) was a Hungarian mathematician.

## Point at infinity

In geometry, a point at infinity or ideal point is an idealized limiting point at the "end" of each line.

## Positional notation

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

## 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.

In number theory, the law of quadratic reciprocity is a theorem about modular arithmetic that gives conditions for the solvability of quadratic equations modulo prime 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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In mathematics and computing, a radix point (or radix character) is the symbol used in numerical representations to separate the integer part of a number (to the left of the radix point) from its fractional part (to the right of the radix point).

## 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 analysis

In mathematics, real analysis is the branch of mathematical analysis that studies the behavior of real numbers, sequences and series of real numbers, and real-valued functions.

## Real number

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

## 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.

## 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 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.

## Rigour

Rigour (British English) or rigor (American English; see spelling differences) describes a condition of stiffness or strictness.

## Ring (mathematics)

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

## Secondary school

A secondary school is both an organization that provides secondary education and the building where this takes place.

## Semigroup

In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative binary operation.

## Semiring

In abstract algebra, a semiring is an algebraic structure similar to a ring, but without the requirement that each element must have an additive inverse.

## Sequence

In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed.

## Series (mathematics)

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.

## Set theory

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

## Sign (mathematics)

In mathematics, the concept of sign originates from the property of every non-zero real number of being positive or negative.

## Signed number representations

In computing, signed number representations are required to encode negative numbers in binary number systems.

## Signed zero

Signed zero is zero with an associated sign.

## Slate (magazine)

Slate is an online magazine that covers current affairs, politics, and culture in the United States from a liberal perspective.

## Stone space

In topology, and related areas of mathematics, a Stone space is a non-empty compact totally disconnected Hausdorff space.

## String (computer science)

In computer programming, a string is traditionally a sequence of characters, either as a literal constant or as some kind of variable.

## Substring

A substring is a contiguous sequence of characters within a string.

## 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.

## Terence Tao

Terence Chi-Shen Tao (born 17 July 1975) is an Australian-American mathematician who has worked in various areas of mathematics.

## Ternary numeral system

The ternary numeral system (also called base 3) has three as its base.

## The Straight Dope

"The Straight Dope" was an online question-and-answer newspaper column published from 1973 to 2018 in the Chicago Reader and syndicated in eight newspapers in the United States.

## Thue–Morse sequence

In mathematics, the Thue–Morse sequence, or Prouhet–Thue–Morse sequence, is the binary sequence (an infinite sequence of 0s and 1s) obtained by starting with 0 and successively appending the Boolean complement of the sequence obtained thus far.

## Timothy Gowers

Sir William Timothy Gowers, (born 20 November 1963) is a British mathematician.

## 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.

## Ultrafinitism

In the philosophy of mathematics, ultrafinitism, also known as ultraintuitionism, strict-finitism, actualism, and strong-finitism, is a form of finitism.

## Ultraproduct

The ultraproduct is a mathematical construction that appears mainly in abstract algebra and in model theory, a branch of mathematical logic.

## Uncountable set

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

## Unit interval

In mathematics, the unit interval is the closed interval, that is, the set of all real numbers that are greater than or equal to 0 and less than or equal to 1.

## Usenet newsgroup

A Usenet newsgroup is a repository usually within the Usenet system, for messages posted from many users in different locations using Internet.

## Winning Ways for your Mathematical Plays

Winning Ways for your Mathematical Plays (Academic Press, 1982) by Elwyn R. Berlekamp, John H. Conway, and Richard K. Guy is a compendium of information on mathematical games.

## World of Warcraft

World of Warcraft (WoW) is a massively multiplayer online role-playing game (MMORPG) released in 2004 by Blizzard Entertainment.