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Bijective numeration, the Glossary

Index 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.[1]

Table of Contents

  1. 31 relations: Addition, Bijection, Decimal, Empty string, Euler summation, Floor and ceiling functions, Gödel numbering, Integer, Leading zero, Logarithm, Malware, Mathematical folklore, Mathematics Magazine, Method of complements, Microsoft Excel, Multiplication, Natural number, Numeral system, P-adic number, P′′, Positional notation, Radix, Shortlex order, Signed-digit representation, Spreadsheet, Unary numeral system, Variable-star designation, 0, 1, 10, 26 (number).

  2. Non-standard positional numeral systems

Addition

Addition (usually signified by the plus symbol) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division.

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Bijection

A bijection, bijective function, or one-to-one correspondence between two mathematical sets is a function such that each element of the first set (the domain) is mapped to exactly one element of the second set (the codomain).

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Decimal

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

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Empty string

In formal language theory, the empty string, or empty word, is the unique string of length zero.

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Euler summation

In the mathematics of convergent and divergent series, Euler summation is a summation method.

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Floor and ceiling functions

In mathematics, the floor function is the function that takes as input a real number, and gives as output the greatest integer less than or equal to, denoted or.

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Gödel numbering

In mathematical logic, a Gödel numbering is a function that assigns to each symbol and well-formed formula of some formal language a unique natural number, called its Gödel number.

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Integer

An integer is the number zero (0), a positive natural number (1, 2, 3,...), or the negation of a positive natural number (−1, −2, −3,...). The negations or additive inverses of the positive natural numbers are referred to as negative integers.

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Leading zero

A leading zero is any 0 digit that comes before the first nonzero digit in a number string in positional notation. Bijective numeration and leading zero are numeral systems.

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Logarithm

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

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Malware

Malware (a portmanteau of malicious software)Tahir, R. (2018).

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Mathematical folklore

In common mathematical parlance, a mathematical result is called folklore if it is an unpublished result with no clear originator, but which is well-circulated and believed to be true among the specialists.

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Mathematics Magazine

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

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Method of complements

In mathematics and computing, the method of complements is a technique to encode a symmetric range of positive and negative integers in a way that they can use the same algorithm (or mechanism) for addition throughout the whole range.

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Microsoft Excel

Microsoft Excel is a spreadsheet editor developed by Microsoft for Windows, macOS, Android, iOS and iPadOS.

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Multiplication

Multiplication (often denoted by the cross symbol, by the mid-line dot operator, by juxtaposition, or, on computers, by an asterisk) is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division.

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Natural number

In mathematics, the natural numbers are the numbers 0, 1, 2, 3, etc., possibly excluding 0.

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Numeral system

A numeral system 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. Bijective numeration and numeral system are numeral systems.

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P-adic number

In number theory, given a prime number, the -adic numbers form an extension of the rational numbers which is distinct from the real numbers, though with some similar properties; -adic numbers can be written in a form similar to (possibly infinite) decimals, but with digits based on a prime number rather than ten, and extending to the left rather than to the right.

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P′′

P′′ (P double prime) is a primitive computer programming language created by Corrado BöhmBöhm, C.: "On a family of Turing machines and the related programming language", ICC Bull.

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Positional notation

Positional notation (or place-value notation, or positional numeral system) usually denotes the extension to any base of the Hindu–Arabic numeral system (or decimal system).

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Radix

In a positional numeral system, the radix (radices) or base is the number of unique digits, including the digit zero, used to represent numbers. Bijective numeration and radix are numeral systems.

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Shortlex order

In mathematics, and particularly in the theory of formal languages, shortlex is a total ordering for finite sequences of objects that can themselves be totally ordered.

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Signed-digit representation

In mathematical notation for numbers, a signed-digit representation is a positional numeral system with a set of signed digits used to encode the integers. Bijective numeration and signed-digit representation are non-standard positional numeral systems.

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Spreadsheet

A spreadsheet is a computer application for computation, organization, analysis and storage of data in tabular form.

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Unary numeral system

The unary numeral system is the simplest numeral system to represent natural numbers: to represent a number N, a symbol representing 1 is repeated N times. Bijective numeration and unary numeral system are numeral systems.

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Variable-star designation

In astronomy, a variable-star designation is a unique identifier given to variable stars.

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0

0 (zero) is a number representing an empty quantity.

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1

1 (one, unit, unity) is a number representing a single or the only entity.

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10

10 (ten) is the even natural number following 9 and preceding 11.

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26 (number)

26 (twenty-six) is the natural number following 25 and preceding 27.

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See also

Non-standard positional numeral systems

References

[1] https://en.wikipedia.org/wiki/Bijective_numeration

Also known as Bijective numeral, Decimal without a zero, Dyadic Encoding, K-adic notation, Proper order.