![]() More elegant is a positional system, also known as place-value notation. In English, one could say "four score less one", as in the famous Gettysburg Address representing "87 years ago" as "four score and seven years ago". However, many languages use mixtures of bases, and other features, for instance 79 in French is soixante dix-neuf ( 60 + 10 + 9) and in Welsh is pedwar ar bymtheg a thrigain ( 4 + (5 + 10) + (3 × 20)) or (somewhat archaic) pedwar ugain namyn un ( 4 × 20 − 1). The number system of the English language is of this type ("three hundred four"), as are those of other spoken languages, regardless of what written systems they have adopted. This system is used when writing Chinese numerals and other East Asian numerals based on Chinese. More useful still are systems which employ special abbreviations for repetitions of symbols for example, using the first nine letters of the alphabet for these abbreviations, with A standing for "one occurrence", B "two occurrences", and so on, one could then write C+ D/ for the number 304. The ancient Egyptian numeral system was of this type, and the Roman numeral system was a modification of this idea. Very commonly, these values are powers of 10 so for instance, if / stands for one, − for ten and + for 100, then the number 304 can be compactly represented as +++ //// and the number 123 as + − − /// without any need for zero. The unary notation can be abbreviated by introducing different symbols for certain new values. Elias gamma coding, which is commonly used in data compression, expresses arbitrary-sized numbers by using unary to indicate the length of a binary numeral. The unary system is only useful for small numbers, although it plays an important role in theoretical computer science. Tally marks represent one such system still in common use. If the symbol / is chosen, for example, then the number seven would be represented by ///////. The simplest numeral system is the unary numeral system, in which every natural number is represented by a corresponding number of symbols. The Hindu-Arabic numeral system then spread to Europe due to merchants trading, and the digits used in Europe are called Arabic numerals, as they learned them from the Arabs. Middle-Eastern mathematicians extended the system to include negative powers of 10 ( fractions), as recorded in a treatise by Syrian mathematician Abu'l-Hasan al-Uqlidisi in 952–953, and the decimal point notation was introduced by Sind ibn Ali, who also wrote the earliest treatise on Arabic numerals. The system slowly spread to other surrounding regions like Arabia due to their commercial and military activities with India. Aryabhata of Kusumapura developed the place-value notation in the 5th century and a century later Brahmagupta introduced the symbol for zero. Indian mathematicians are credited with developing the integer version, the Hindu–Arabic numeral system. The most commonly used system of numerals is decimal. Such systems are, however, not the topic of this article. ![]() Numeral systems are sometimes called number systems, but that name is ambiguous, as it could refer to different systems of numbers, such as the system of real numbers, the system of complex numbers, the system of p-adic numbers, etc.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |