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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. [1]

74 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, If and only if, India, Integer, Language, 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, P-adic number, ... Expand index (24 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 the function or operation accepts.

## Aryabhata

Aryabhata (आर्यभट; 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 every element of one set is paired with exactly one element of the other set, and every 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 binary numeral system, or base-2 numeral system, which represents numeric values using two different symbols: typically 0 (zero) and 1 (one).

## Bit

A bit is the basic unit of information in computing and digital communications.

## Brahmagupta

Brahmagupta (ब्रह्मगुप्त) (598–c.670 CE) was an Indian mathematician and astronomer who wrote two works on mathematics and astronomy: the Brāhmasphuṭasiddhānta (Extensive Treatise of Brahma) (628), a theoretical treatise, and the Khaṇḍakhādyaka, a more practical text.

## 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 the imaginary unit, that satisfies the equation.

## Computer

A computer is a general-purpose device that can be programmed to carry out a set of arithmetic or logical operations automatically.

## 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 digital 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 10 or occasionally denary) has ten as its base.

## 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 in 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 is the ordering or sequencing of bytes of a word of digital data in computer memory storage or during transmission.

## 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, one of the best-known in American history.

## GNU Multiple Precision Arithmetic Library

The 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+)/2 ≈ 1.61803399 symbolized by the Greek letter φ) as its base.

## Greek numerals

Greek numerals are a system of representing 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 numeral system or Hindu–Arabic numeral systemDavid Eugene Smith and Louis Charles Karpinski,, 1911 is a positional decimal numeral system, nowadays the most common symbolic representation of numbers in the world.

## 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.

## India

India, officially the Republic of India, is a country in South Asia.

## 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 the ability to acquire and use complex systems of communication, particularly the human ability to do so, and a language is any specific example of such a system.

## 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 operation 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:;Long scale: Every new term greater than million is one million times larger than the previous term.

## 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 (sometimes called the whole numbers): "whole number An integer, though sometimes it is taken to mean only non-negative integers, or just the positive integers." give definitions of "whole number" under several headwords: INTEGER … Syn. whole number.

## Number

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

## Numeral (linguistics)

In linguistics, a numeral is a member of a word class (or sometimes even a part of speech) designating numbers, such as the English word 'two' and the compound 'seventy-seven'.

## 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 digit is a numeric symbol (such as "2" or "5") used in combinations (such as "25") to represent numbers (such as the number 25) in 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

Orders of magnitude are written in powers of 10.

## 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 way different 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, the ratio of a circle's circumference to its diameter, commonly approximated as 3.14159.

## 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 has no positive divisors other than 1 and itself.

## Punycode

Punycode is a way to represent Unicode with the limited character subset of ASCII supported by the Domain Name System.

## Quater-imaginary base

The quater-imaginary numeral system was first proposed by Donald Knuth in 1955, in a submission to a high-school science talent search.

## Quipu

Quipus, sometimes known as khipus or talking knots, were recording devices historically used 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 p/q of two integers, p and q, with the denominator q not equal to zero.

## Real number

In mathematics, a real number is a value that represents a quantity along a continuous line.

## Repeating decimal

A repeating or recurring decimal is a way of representing rational numbers in base 10 arithmetic.

## Residue numeral 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

Roman numerals, the numeric system used in ancient Rome, employs combinations of letters from the Latin alphabet to signify values.

## Sequence

In mathematics, a sequence is an ordered 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 is a division or subset of general computer science and mathematics that focuses on more abstract or mathematical aspects 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, word is a term for 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 (number)

0 (zero; BrE: or AmE) is both a number and the numerical digit used to represent that number in numerals.

## References

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