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Encyclopedia > Unary numeral system
Numeral systems

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The unary numeral system is the simplest numeral system to represent natural numbers: in order to represent a number N, an arbitrarily chosen symbol is repeated N times. For example, using the symbol "|" (a tally mark), the number 6 is represented as "||||||". The standard method of counting on one's fingers is effectively a unary system. Unary is most useful in counting or tallying ongoing results, such as the score in a game of sports, since no intermediate results need to be erased or discarded. Jump to: navigation, search A numeral is a symbol or group of symbols that represents a number. ... Jump to: navigation, search Natural number can mean either a positive integer (1, 2, 3, 4, ...) or a non-negative integer (0, 1, 2, 3, 4, ...). Natural numbers have two main purposes: they can be used for counting (there are 3 apples on the table), and they can be used... Tally marks are a variation of the unary numeral system. ... Counting is the mathematical action of adding (or subtracting) one, usually to find out how many objects there are or to set aside a desired number of objects (starting with one for the first object and proceeding with a one-to-one correspondence); however, counting is also used (primarily by... Score can mean one of several things: Look up score in Wiktionary, the free dictionary. ...

Addition and subtraction are particularly simple in the unary system, as they involve little more than string concatenation. Multiplication and division are more cumbersome, however. Addition (or summation) is one of the basic operations of arithmetic. ... Jump to: navigation, search In mathematics, subtraction is one of the four basic arithmetic operations. ... In various branches of mathematics and computer science, strings are sequences of various simple objects (symbols, tokens, characters, etc. ... In its simplest form, multiplication is the sum of a list of identical numbers. ... Jump to: navigation, search In mathematics, especially in elementary arithmetic, division is an arithmetic operation which is the reverse operation of multiplication, and sometimes it can be interpreted as repeated subtraction. ...

Compared to positional numeral systems, the unary system is inconvenient and is not used in practice for large calculations. It occurs in some decision problem descriptions in theoretical computer science (e.g. some P-complete problems), where it is used to "artificially" decrease the run-time or space requirements of a problem. For instance, the problem of integer factorization is suspected to require more than a polynomial function of the input as run-time if the input is given in binary, but it only needs linear runtime if the input is presented in unary. But this is potentially misleading: using a unary input is slower for any given number, not faster; the distinction is that a binary (or larger base) input is proportional to the base 2 (or larger base) logarithm of the number while unary input is proportional to the number itself; so while the run-time and space requirement in unary looks better as function of the input size, it is a worse function of the number that the input represents. Jump to: navigation, search A numeral is a symbol or group of symbols that represents a number. ... In logic, a decision problem is determining whether or not there exists a decision procedure or algorithm for a class S of questions requiring a Boolean value (i. ... Computation can be defined as finding a solution to a problem from given inputs by means of an algorithm. ... In complexity theory, the complexity class P-complete is a set of decision problems and is useful in the analysis of which problems can be efficiently solved on parallel computers. ... In number theory, the integer factorization problem is the problem of finding a non-trivial divisor of a composite number; for example, given a number like 91, the challenge is to find a number such as 7 which divides it. ... Jump to: navigation, search The binary numeral system represents numeric values using two symbols, typically 0 and 1. ...

For a real example of the unary system in ancient mathematics, see the Moscow Mathematical Papyrus, dating from circa 1800 BC. Jump to: navigation, search The Moscow and Rhind Mathematical Papyri are two of the oldest mathematical texts and perhaps our best indication of what ancient Egyptian mathematics might have been like near 2000 BC. They are both written on papyrus. ... (Redirected from 1800 BC) (19th century BC - 18th century BC - 17th century BC - other centuries) (3rd millennium BC - 2nd millennium BC - 1st millennium BC) Events 1787 - 1784 BC -- Amorite conquests of Uruk and Isin 1786 BC -- Egypt: End of Twelfth Dynasty, start of Thirteenth Dynasty, start of Fourteenth Dynasty 1766...

Dr. Melzak's Q machines, a simplification of Turing machines, basically a set of bottomless pits containing stones, work with the unary number system.

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