Mathematics in Ancient and Medieval India c5.s2: Classification of Numbers
Mathematics in Ancient and Medieval India c5.s2
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Classification of Numbers
c5.s2.1
Classification of numbers into odd and even first appeared in the Vedic literature.¹ The classification also appeared in the Jaina works but the authors did not consider unity a number like the ancient Greeks. In the Jaina work, *Anuyogadvārasūtra*², the numbers were classified also as numerable ( *saṃkhyeya* ), innumerable ( *asaṃkhyeya* ) and infinite ( *ananta* ). The highest numerable number of the Jaina corresponds to Alef-zero³ of the modern mathematics and they also made an attempt to define number beyond Alef-zero. As regards innumerable number, names of several sub-classifications were mentioned but the idea was not very clear. Idea of infinity was expressed in connection with different dimensions namely infinity in one, two, three and infinite dimensions.
c5.s2.2
¹ *Taittirīya Saṃhitā*, 7. 2. 12-13.
c5.s2.3
² Datta, B. 'The Jaina School of Mathematics', *Bulletin of the Calcutta Math. Society*, 21, p. 136-38, 1929.
c5.s2.4
³ The cardinal number of the aggregates of all the finite integers 1, 2, 3, ...... n is called Alef-Zero. The theory of such numbers was fully developed by G. Cantor in 1883 A. D.
Linked texts (2)
- Taittirīyasaṃhitā — Sanskrit
- Aṇuogaddārāiṃ — Āryarakṣita, Ardhamāgadhī Prakrit