Basic Mathematics

Author(s): L C Jain
Publisher: Rajasthan Prakrit Bharti Sansthan Jaipur

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of Pingala's work Chanda Sūtra—a work on prosody before 200 B. C.
It is said that the concept of infinity in mathematics was conceived for the first time by the Indian mathematician Brahmagupta (c. 628 A. D.) while in the western countries, this credit goes to Bernhard Bolzano of the 19th century A. D. A study of infinity in mathematics as a mature concept was however taken up by Bhāskarācārya (c. 1150 A. D. He appears to be the first mathematician to have deduced the value of the quotient a mathematically where a is a finite quantity and termed it as ananta. But the description of infinity as endless or countless can be traced in Rgveda and many other ancient works including those by Jaina and Buddhist scholars. An elaborate classification and philosophical explanation of infinity (ananta) is however found in the Jaina canonical texts as old as 300-400 B. C. where infinity of even ten types has been mentioned, e. g. in the Sthānanga-Sūtra (325 B. C.), Uttarādhyana-Sūtra (300 B. C.). The idea of infinity has been combined with that of dimensions, e, g., infinity in one direction ( at ata), infinity in two directions (francia), infinity in area (agt fararttaa), infinity everywhere (a faFAITTC) and infinity perpetual (Paaha). It is mentioned that : अथवा पंच विद्या अनंत प्रज्ञप्ता: तद्यथा एकतो अनंतम् द्वि विधानन्तं, देश faxatira, qafarar, array. While in Dhavalā and some other Jain philosphical texts, ten types of infinity have been described, e. g., nominal attributed, fluent, numerical, diamensionless, mono, bi, areal, spatial, phase and indestructible (everlasting).
In Kalpa-Sūtra and Navatattva (both works of 300 B. C.) infinity is described as a number as great as the number of sand grains on the brinks of all rivers on the earth or the drops of water in all the oceans. The
Tilloypaņņatti, another important Jaina text, deals with infinity under mathematical disciplines. The Jaina concept of infinity in Mathematics can be explained in modern technology as, “If the law of variation of a magnitude x is such that it becomes and remains greater than any pre-assigned magnitude, however large, then x is said to become infinite and this concept is denoted by co
The Jaina works on mathematics also deal with rules of operations with numbers, permutations and combinations, solutions of simultaneous equations, indeterminate equations of the first degree, laws of indices, arithmetical and geometrical progressions, rules for operation with infinity, mensuration formulae for different surfaces and solid bodies and many other topics.
In Chapter I on Introduction of this book, the author has mentioned
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