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- The journey of numerals began in ancient civilizations, where the need for record-keeping and trade necessitated a system to represent quantities. Early numerals were often simple marks – tally marks carved on wood or bone, like the Ishango bone. As societies grew more complex, so did their numeral systems.
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History. The first true written positional numeral system is considered to be the Hindu–Arabic numeral system. This system was established by the 7th century in India, [1] but was not yet in its modern form because the use of the digit zero had not yet been widely accepted.
- Overview
- The Hindu-Arabic system
- The binary system
Several different claims, each having a certain amount of justification, have been made with respect to the origin of modern Western numerals, commonly spoken of as Arabic but preferably as Hindu-Arabic. These include the assertion that the origin is to be found among the Arabs, Persians, Egyptians, and Hindus. It is not improbable that the intercourse among traders served to carry such symbols from country to country, so that modern Western numerals may be a conglomeration from different sources. However, as far as is known, the country that first used the largest number of these numeral forms is India. The 1, 4, and 6 are found in the Ashoka inscriptions (3rd century bce); the 2, 4, 6, 7, and 9 appear in the Nana Ghat inscriptions about a century later; and the 2, 3, 4, 5, 6, 7, and 9 in the Nasik caves of the 1st or 2nd century ce—all in forms that have considerable resemblance to today’s, 2 and 3 being well-recognized cursive derivations from the ancient = and ≡. None of these early Indian inscriptions gives evidence of place value or of a zero that would make modern place value possible. Hindu literature gives evidence that the zero may have been known earlier, but there is no inscription with such a symbol before the 9th century.
The first definite external reference to the Hindu numerals is a note by Severus Sebokht, a bishop who lived in Mesopotamia about 650. Since he speaks of “nine signs,” the zero seems to have been unknown to him. By the close of the 8th century, however, some astronomical tables of India are said to have been translated into Arabic at Baghdad, and in any case the numeral became known to Arabian scholars about this time. About 825 the mathematician al-Khwārizmī wrote a small book on the subject, and this was translated into Latin by Adelard of Bath (c. 1120) under the title of Liber algorismi de numero Indorum. The earliest European manuscript known to contain Hindu numerals was written in Spain in 976.
Several different claims, each having a certain amount of justification, have been made with respect to the origin of modern Western numerals, commonly spoken of as Arabic but preferably as Hindu-Arabic. These include the assertion that the origin is to be found among the Arabs, Persians, Egyptians, and Hindus. It is not improbable that the intercourse among traders served to carry such symbols from country to country, so that modern Western numerals may be a conglomeration from different sources. However, as far as is known, the country that first used the largest number of these numeral forms is India. The 1, 4, and 6 are found in the Ashoka inscriptions (3rd century bce); the 2, 4, 6, 7, and 9 appear in the Nana Ghat inscriptions about a century later; and the 2, 3, 4, 5, 6, 7, and 9 in the Nasik caves of the 1st or 2nd century ce—all in forms that have considerable resemblance to today’s, 2 and 3 being well-recognized cursive derivations from the ancient = and ≡. None of these early Indian inscriptions gives evidence of place value or of a zero that would make modern place value possible. Hindu literature gives evidence that the zero may have been known earlier, but there is no inscription with such a symbol before the 9th century.
The first definite external reference to the Hindu numerals is a note by Severus Sebokht, a bishop who lived in Mesopotamia about 650. Since he speaks of “nine signs,” the zero seems to have been unknown to him. By the close of the 8th century, however, some astronomical tables of India are said to have been translated into Arabic at Baghdad, and in any case the numeral became known to Arabian scholars about this time. About 825 the mathematician al-Khwārizmī wrote a small book on the subject, and this was translated into Latin by Adelard of Bath (c. 1120) under the title of Liber algorismi de numero Indorum. The earliest European manuscript known to contain Hindu numerals was written in Spain in 976.
There is one island, however, in which the familiar decimal system is no longer supreme: the electronic computer. Here the binary positional system has been found to have great advantages over the decimal. In the binary system, in which the base is 2, there are just two digits, 0 and 1; the number two must be represented here as 10, since it plays the same role as does ten in the decimal system. The first few binary numbers are displayed in the table.
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Numbers and Mathematics
A binary number is generally much longer than its corresponding decimal number; for example, 256,058 has the binary representation 111 11010 00001 11010. The reason for the greater length of the binary number is that a binary digit distinguishes between only two possibilities, 0 or 1, whereas a decimal digit distinguishes among 10 possibilities; in other words, a binary digit carries less information than a decimal digit. Because of this, its name has been shortened to bit; a bit of information is thus transmitted whenever one of two alternatives is realized in the machine. It is of course much easier to construct a machine to distinguish between two possibilities than among 10, and this is another advantage for the base 2; but a more important point is that bits serve simultaneously to carry numerical information and the logic of the problem. That is, the dichotomies of yes and no, and of true and false, are preserved in the machine in the same way as 1 and 0, so in the end everything reduces to a sequence of those two characters.
Feb 23, 2024 · The history of numbers begins with early humans, whose survival depended on the ability to keep track of vital resources like food and livestock. Imagine a prehistoric human using tally marks on a cave wall or a bone, like the famous Ishango bone from Africa, to record quantities.
Number systems have progressed from the use of fingers and tally marks, perhaps more than 40,000 years ago, to the use of sets of glyphs able to represent any conceivable number efficiently. The earliest known unambiguous notations for numbers emerged in Mesopotamia about 5000 or 6000 years ago.
Have you ever wondered how numbers first came about? Using only ten symbols (0 – 9), we can write and rational number imaginable. But why do we use these ten symbols? And why is there 10 of them? Strange as it seems to us now, there was a time when numbers, as we know them, simply weren’t invented.
These symbols appeared in Egypt as early as 3400 bce and in Mesopotamia as early as 3000 bce, long preceding the first known inscriptions containing numerals in China (c. 1600 bce), Crete (c. 1200 bce), and India (c. 300 bce). Some ancient symbols for 1 and 10 are shown here.
It appears that the primitive numerals were |, ||, |||, and so on, as found in Egypt and the Grecian lands, or ―, =, ≡, and so on, as found in early records in East Asia, each going as far as the simple needs of people required.
