Basic Mathematics

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

Page 42

The earlier above is the description of simile measure in Jainology, with the help of which space and time measures are given in terms of cardinal numbers of sets.
(b) Number Measure :
For a modern mathematician, there is no need of a well-defined word “number". However it could be stated generally that a number is a set of equivalent sets alone. This would include all types of rational, transcendental, irrational, natural and integer numbers.
During the Pythagorean era, discussions on infinity had been initiated, but arguments or paradoxes of Zeno (+5th century) had created fear in moving towards analysis of infinities. After Galileo (+1564 to +1642) when George Cantor (+ 1845 to +1918) started his work on infinities and sets, the mathematician began to say that this subject has been brought 100 years too early, 56 Whereas, in India this had reached its climax even before the early centuries of Christian Era.57
The Jaina School needed a quantitative analysis of Karmic events, for which new mathematical but proper infinity was to play an important role. Through a long process, twentyone types of ranges were produced by carrying on certain types of multiplication, squaring as well as by adding or projecting various types of sets (in cardinal or in ordinal lay out). These ranges gave twenty one types of divisions of new mathematical infinity ranging from unity to the cardinal number of the indivisible-corresponding-sections of Omniscience (all knowledge or Kevalajñāna).58
1. Samkhyāta (Numerable)
1.1. Jaghanya (Minimal) 1.2. Madhyama (Intermediate) 1.3. Utkrsta (Maximal)
2. Asamkhyāta (Innumerable) 2.1. Parita (Extended)
2.1.1. Jaghanya 2.1.2. Madhyama 2.1.3. Utkrsta
2.2. Yukta (Yoked)
2.2.1. Jaghanya 56. Cf. Fraenkel, A. A, Abstract Set Theory, Amsterdam, 1953. 57. Jain, L. C., Set Theory in Jaina School of Mathematics, I.J. H. S.,
Vol. 8, nos. 1 & 2, 1973, 1-27. 58. Cf. T.P.G., pp. 55 et, seq.
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