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# 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. 

76 relations: -yllion, Addison-Wesley, Alfred L. Kroeber, Arithmetic progression, Arity, Aryabhata, Bijection, Bijective numeration, Binary number, Bit, Brahmagupta, Cantor set, Chinese numerals, Complex number, Computer, Computer number format, Data compression, Decimal, Donald Knuth, Egyptian numerals, Elias gamma coding, Endianness, English language, Finite set, Geometric progression, Gettysburg Address, GNU Multiple Precision Arithmetic Library, Golden ratio base, Greek numerals, Hexadecimal, Hindu–Arabic numeral system, History of ancient numeral systems, If and only if, Integer, Language, List of Indian mathematicians, List of numeral system topics, List of numeral systems, Logarithm, Long and short scales, Mathematical notation, Mixed radix, Natural number, Number, Numeral (linguistics), Numerical cognition, Numerical digit, Octal, Order of magnitude, Overline, ... Expand index (26 more) »

## -yllion

-yllion is a proposal from Donald Knuth for the terminology and symbols of an alternate decimal superbase system.

Addison-Wesley is a publisher of textbooks and computer literature.

## Alfred L. Kroeber

Alfred Louis Kroeber (June 11, 1876 – October 5, 1960) was an American cultural anthropologist.

## Arithmetic progression

In mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

## Arity

In logic, mathematics, and computer science, the arity of a function or operation is the number of arguments or operands that the function takes.

## Aryabhata

Aryabhata (IAST) or Aryabhata I (476–550 CE) was the first of the major mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy.

## 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.

## Bijective numeration

Bijective numeration is any numeral system in which every non-negative integer can be represented in exactly one way using a finite string of digits.

## 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).

## Bit

The bit (a portmanteau of binary digit) is a basic unit of information used in computing and digital communications.

## Brahmagupta

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

## 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.

## Chinese numerals

Chinese numerals are words and characters used to denote numbers in Chinese.

## 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.

## Computer

A computer is a device that can be instructed to carry out sequences of arithmetic or logical operations automatically via computer programming.

## Computer number format

A computer number format is the internal representation of numeric values in digital computer and calculator hardware and software.

## Data compression

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

## 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.

## Donald Knuth

Donald Ervin Knuth (born January 10, 1938) is an American computer scientist, mathematician, and professor emeritus at Stanford University.

## Egyptian numerals

The system of ancient Egyptian numerals was used in Ancient Egypt from around 3000 BC until the early first millennium AD.

## Elias gamma coding

Elias gamma code is a universal code encoding positive integers developed by Peter Elias.

## Endianness

Endianness refers to the sequential order in which bytes are arranged into larger numerical values when stored in memory or when transmitted over digital links.

## English language

English is a West Germanic language that was first spoken in early medieval England and is now a global lingua franca.

## Finite set

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

## Geometric progression

In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

The Gettysburg Address is a speech by U.S. President Abraham Lincoln, and one of the best-known speeches in American history.

## GNU Multiple Precision Arithmetic Library

GNU Multiple Precision Arithmetic Library (GMP) is a free library for arbitrary-precision arithmetic, operating on signed integers, rational numbers, and floating point numbers.

## 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.

## 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.

In mathematics and computing, hexadecimal (also base, or hex) is a positional numeral system with a radix, or base, of 16.

## Hindu–Arabic numeral system

The Hindu–Arabic numeral systemDavid Eugene Smith and Louis Charles Karpinski,, 1911 (also called the Arabic numeral system or Hindu numeral system) is a positional decimal numeral system that is the most common system for the symbolic representation of numbers in the world.

## History of ancient numeral systems

Numeral systems have progressed from the use of tally marks, more than 40,000 years ago, through to the use of sets of glyphs to efficiently represent any conceivable number.

## If and only if

In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements.

## 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").

## Language

Language is a system that consists of the development, acquisition, maintenance and use of complex systems of communication, particularly the human ability to do so; and a language is any specific example of such a system.

## List of Indian mathematicians

The chronology of Indian mathematicians spans from the Indus Valley Civilization and the Vedas to Modern India.

## List of numeral system topics

This is a list of Wikipedia articles on topics of numeral system and "numeric representations" See also: computer numbering formats and number names.

## List of numeral systems

This is a list of numeral systems, that is, writing systems for expressing numbers.

## Logarithm

In mathematics, the logarithm is the inverse function to exponentiation.

## Long and short scales

The long and short scales are two of several large-number naming systems for integer powers of ten that use the same words with different meanings.

## Mathematical notation

Mathematical notation is a system of symbolic representations of mathematical objects and ideas.

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

## 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").

## Number

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

## 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'.

## 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.

## Octal

The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7.

## 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.

## Overline

An overline, overscore, or overbar, is a typographical feature of a horizontal line drawn immediately above the text.

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.

## Patna

Patna is the capital and largest city of the state of Bihar in India.

## Pi

The number is a mathematical constant.

## 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.

## Punycode

Punycode is a representation of Unicode with the limited ASCII character subset used for Internet host names.

## Quater-imaginary base

The quater-imaginary numeral system was first proposed by Donald Knuth in 1960.

## Quipu

Quipu (also spelled khipu) or talking knots, were recording devices fashioned from strings historically used by a number of cultures, particularly in the region of Andean South America.

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.

## 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 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.

## Residue number system

A residue numeral system (RNS) represents a large integer using a set of smaller integers, so that computation may be performed more efficiently.

## Roman numerals

The numeric system represented by Roman numerals originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages.

## Scientific notation

Scientific notation (also referred to as scientific form or standard index form, or standard form in the UK) is a way of expressing numbers that are too big or too small to be conveniently written in decimal form.

## Sequence

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

## Sign-value notation

A sign-value notation represents numbers by a series of numeric signs that added together equal the number represented.

## Subtractive notation

Subtractive notation is an early form of positional notation used with Roman numerals as a shorthand to replace four or five characters in a numeral representing a number with usually just two characters.

## Tally marks

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

## The Art of Computer Programming

The Art of Computer Programming (sometimes known by its initials TAOCP) is a comprehensive monograph written by Donald Knuth that covers many kinds of programming algorithms and their analysis.

## Theoretical computer science

Theoretical computer science, or TCS, is a subset of general computer science and mathematics that focuses on more mathematical topics of computing and includes the theory of computation.

## Unary numeral system

The unary numeral system is the bijective base-1 numeral system.

## Weight function

A weight function is a mathematical device used when performing a sum, integral, or average to give some elements more "weight" or influence on the result than other elements in the same set.

## Word (computer architecture)

In computing, a word is the natural unit of data used by a particular processor design.

## Writing system

A writing system is any conventional method of visually representing verbal communication.

## 0

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

## References

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