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12. Mathematical Form of Paramāņu-units
(Vargaṇā) According to Acārānga sūtra
Vargana is nothing but a type of paramāņu-units, possessing the same num
ber of paramāņus.
The first Vargaṇā means individual paramāņus which have separate existence in the universe from each other. A second Vargaṇā means all paramāņuunits throughout the universe which have only two paramāņus. In the same way, there are other Vargaṇās possessing paramāņu-units having 3, 4, 5, ... innumerable paramāņus.
But these Vargaṇās are not useful for Audārika bodies. Even the paramāņuunits having infinite paramāņus are not useful for Audārika bodies. Suppose this infinite number is denoted as 'a,". After these infinite numbers of Vargaṇās, there are some useful Vargaņās possessing the paramāņu-units having the number of paramāņus a,+1, a,+2, a,+3,.... a,+a",, where a, > a,, but a", is also infinite. These Vargaṇās are useful for Audārika bodies and they are also called Audārika Vargaṇā.
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After a,+a',, there are many unuseful Vargaṇās, e.g. a,+a”,+1, a,+a”, +2, a,+a",+3, a,+a+a”,. Here a", > a,+a", All these are not useful for Audārika bodies due to greater number of paramāņus, and also not useful for Vaikriya bodies due to greater size of paramāņus.
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Now we assume that a,+a′,+a”, = a,, then a2+1, a2+2, a2+3, a2+a2 Varganās are useful for Vaikriya bodies, where a, > a", Vargaṇās a2+a'2+1, à ̧±à ́¿+2, à ̧±à ́ ̧+з, ... a2+a+a”, are unuseful for Vaikriya bodies due to their greater number of paramāņus and also unuseful for Āhāraka bodies due to their greater size of the paramāņus. Here also a", > a, + a',
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Now we will take a2+a+a"2 = a, is unuseful Vargaṇā for Vaikriya and Ahāraka bodies. Then a,+1, a,+2, a2+3, a+a, are useful Vargaṇās for Āhāraka bodies (here a, > a"). And a,+a+1‚a ̧±à ́ ̧+2, à ̧±à ́ ̧+3, ... a2+a ́ ̧+a′ are unuseful for Aharaka bodies due to their smaller size of paramāņus and
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