[Pramāṇa](https://indike.org/pramana/) › [Studies](https://indike.org/pramana/ins) › [Science, technology and education](https://indike.org/pramana/ins.science) › [Mathematics in Ancient and Medieval India](https://indike.org/pramana/ins.science.bag-1979) › c5.s2 # Mathematics in Ancient and Medieval India c5.s2: Classification of Numbers Mathematics in Ancient and Medieval India c5.s2 - **Language:** English ### Classification of Numbers ### [c5.s2.1](https://indike.org/pramana/ins.science.bag-1979.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](https://indike.org/pramana/ins.science.bag-1979.c5.s2.2) ¹ \*Taittirīya Saṃhitā\*, 7. 2. 12-13. ### [c5.s2.3](https://indike.org/pramana/ins.science.bag-1979.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](https://indike.org/pramana/ins.science.bag-1979.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. ## Cites (2) - [Kṛṣṇayajurvedasaṃhitā](https://indike.org/pramana/in.veda.samhita.krsnayajur*taittiriya.7.2.12) — Sanskrit - [Aṇuogaddārāiṃ](https://indike.org/pramana/in.jaina.sveta.cullika.2) — Āryarakṣita, Ardhamāgadhī Prakrit --- Source: [https://indike.org/pramana/ins.science.bag-1979.c5.s2](https://indike.org/pramana/ins.science.bag-1979.c5.s2) · Pramāṇa