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Mathematical Expositions of Vīrasena in Dhavalā Commentary : (201)
the value of maximal numerable number is sufficiently higher and variable than presented in Dhavalā.
Beyond the numerable, comes the innumerable (As), which has eleven varieties vide verse 3.57 p. 123. Out of which, the countable innumerable is important for us. It has three varieties: (1) Peripheral (Parīta), (2) Yoked (Yukta) and (3) Innumerable (i). Each of them has three varieties: (1) Minimal (2) Maximal and (3) Medial. The author has used the medial innumerable innumerate number in his discussions and calculation (Vol.3, p. 127). The value of innumerable number is normally calculated on the basis of pit-based simile measures called Palyopama (P) and Sāgaropama (S) - a unit of 109 P. However, Vīrasena has given another method to express innumerable in which it lies between
Minimal As. As (P/As) and Minimal peripheral infinity + (innumerable universe)? Both the terms are incalculable. However, Muni Mahendra?has calculated the minimum value of Palyopama“ (P) as 4.1X1040-31 which could be converted into S-units by multiplying it with 10".
The minimal peripheral innumerable = maximal numerable number + 1.
Generally, the upper unit is larger by 1 than its adjacent lower unit and the lower unit is lesser by one than its adjacent upper unit.
Vīrasena (Dhavalā 3, p.11) has improved the concept of five or ten-fold infinity of Th. (5.217; 10.66) to 11-fold one by adding mode of knowledge to it. It has been eleven-foldly classified as the innumerable. Out of them, the countable infinity (numerical infinity) is of concern to us, which has a large description. It has also the varieties as in the case of innumerable each divided into three classes each. The quantitative description with reference to infinity refers to medial infinite-infinite class. It could be guessed that Minimal peripheral Infinite number = Maximal innumerable innumerable + 1
However, Vīrasena has given the following formula for the value of medial infinite-infinite. Let the minimal infinite-infinite be n, then squared-squaring it three times, we get
n adm-11 n+n" → (n") "" + (n")******* If this method is applied in case of the number 2, we get,
22 + 4 + 256236 +617 digit number
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