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karmic system in their canonical texts with the help of very gigantic numbers or infinite numbers. In order to treat such numbers and give them compact expression, they developed a powerful operation called vargana samavargana. The process of the operation occurs in the DVL.6 Some other references are the TP (v. 4, 310-313, pp. 89-94) and TLS (v. 48, p. 46).
It is composed of the following three operations.
[a] Viralana (Distribution)
the number into its unities.
For instance,
where a > 1.
[b] Deya (Substitution)
the number in the place everywhere in the distribution of the number.
For instance,
etc.
V(a) =1 | | |
The viralana (V) of a number means to distribute
[c] Gunana (Multiplication)
all the substitutes.
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For instance,
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The deya (D) of a number means to substitute
D[V(a)] = a a a a...... ...a times.
-
G[D(V(a))] = a.a.a.a.............a times.
The result thus obtained is simply called vargita samavargita (abbreviated. as VSV) of the number. In a modern style, we can write the same as
VSV (a) = a".
a is called the first vargita samavargila (or 1 VSV) of the number 'a' when the operation of the vargita samavargita is to be repeated to successive orders. Further, we have
a times
The gunana (G) means to multiply mutually
(a)
2VSV (a) (a)
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3VSV (a):
=
The operation can be repeated to various orders but the DVL does not contemplate its application more than the order three.
L.C. Jain (1958, pp. 9 and 59 and 1982, p. 30) seems to be the first mathematician to have denoted the vargita samavargita of a number
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