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Mathematical Expositions of Vīrasena in Dhavalā Commentary : (199)
Expression of Numbers
The numbers have been expressed through digits Devanagari alphabets and words. Besides digits, Vīrasena has used words and alphabets representing number (also some Jinistic principles) in many places as seen in verse 3.71 of Vol. 3:
Akāśa
Kaṣāya
Khara
Acala
Candra
Nabha
0
16
6
7
1
0
(Space) (Passions)
-
(Mountains)
(Moon)
(Space)
Naya
Mrgänka
Dravya
Padartha
Rtu
Basu
Jain Education International
2
(Standpoints)
1
(Moon)
6
(Realities)
9
(Reals)
6 (Season)
8
Classification and Definition of Numbers
In the first instance, the numbers have been two-foldly classified in terms of odd (Oja) and even (Yugma)-each two-foldly subclassified as below vide Vol. 3, p. 249 and Vol. 10 page 222-23.
Even numbers
(1) Without remainder when divided by 4. (2) With a remainder of 2 when divided by 4. Odd Numbers
(1) With a remainder of 1 when divided by 4. (2) With a remainder of 3 when divided by 4.
Their technical names are not given here. However, the basis of 4 for this classification needs consideration. For practical purposes, this may be only an intellectual classification prior to other classifications.
In the second stage, the Jain scholars have three-foldly classified the numbers: (1) Numerable (2) Innumerable and (3) Infinite. All these varieties have been defined sub-classified and detailed in Jaina religious texts. Dhavalā (Vol. III, p. 267) has defined the terms as below:
(1) Numerable: Objects of five cognitive senses or vocable knowledge; a number, which could be counted.
(2) Innumerable: Objects of clairvoyance: a number which could end or finish by one-by-one subtraction.
(3) Infinite: Objects of omniscience; a number, which could never end by one-by-one subtraction.
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