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(202) : Nandanavana
Multiplying this number by infinity n and subtracting the infinite times the projected number of six reals (dravyas) from it, we get the value of medial infinite-infinite or
medial infinite-infinite = n(n")" -n (projected number of six reals) or the value lies between (n)" and (nmax)". Similar point has been referred in case of medial innumerable. Singh and Jain have pointed out that the Jainas have given dimensions also to infinity (mono, dietc.)
Thus, we get 3 numerables, 9 innumerables and nine infinite numbers in Jain number system, making 21 in all (20 as per ADS, the maximal infinite-infinite not agreed). All these numbers have been used as multiplier-factors (gunakaras) for computing the measures of the living and non-living entities in different places in the commentary. Expression of Large Numbers
Dhavalā has given four methods for expressing and calculating large numbers: (1) Place-value notation based on ten (or 100 in some cases), (2) Squared squaring (S-S), (3) Triadic-Salāka-based operation and (4) use of log2 or log.log2 etc. Thus all the methods indicate the knowledge of the law of indices by Vīrasena.
The first method is popular and needs not be illustrated here. The second method can be expressed in terms of once, twice and thrice SS of 2 as below:
2_1" sS >22_2nd SS 4* _3rd SS (256) 256 In algebraic terms, if the number is n, then
the 3rd S.S. of n= (n" n(n+l+n*tly In most cases, the calculations have gone up to 3 SS yielding a very large or sometimes infinite number in case of 2, it contain 617 digits).
The third method yields still larger numbers. For example, we assume the basic salāka number as 4. It is squared-squared once, (4) = 256. We deduce one from 4, (4-1=3). The number 256 is again squared-squared to yield a 617 digit number, say x. We again deduce 1 from 3, (3-1=2). The last number obtained in this way is again
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