Counting Systems

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The first operation to be considered is numeration, which is defined in a rather modern vein as the representation of numbers by symbols. To fully appreciate the task the Treviso's author is undertaking in this section, one should understand the level of acceptance for the "Hindu-Arabic" numeral system that existed in Europe at this time (Al-Daffa, 1977)..


There was a certain social status and prestige associated with the use of a counting table.
Hindu mathematics presents interesting features of notation. Valuable information on this development is revealed by the Bakhsh'l' Manuscript. First, Hindu Arabic numeral system was mentioned in the 9th century. It is classified as a positional decimal numeral system consisted of symbols (Smith and Karpinski 1911). It has been generally believed that the so-called Arabic numerals, from which arise those in use by us today, were derived by the Muslim peoples from India, and that the Hindus invented (1) the principle of position or place value of the decimal point and (2) the nine digits and zero (or dot). In the astrological treatise written by Ch''-t'an Hsi-ta, who flourished under the T'ang Dynasty in the early eighth century A.D., the so-called Hindu decimal notation and rules are implied, so that they were introduced, or re-introduced into China, at that time or possibly earlier (Datta and Singh 1998).
Whereas Hindu astronomy made improvement through Greek influence, mathematics in India, as Professor Sarton has stated, had no need to wait for Hellenism: we are, therefore, at present disinclined to refuse legitimate claims for Hindu originality in respect of the nine numerals and decimal system (Al-Daffa, 1977). ...
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