Basic Mathematics

Author(s): L C Jain
Publisher: Rajasthan Prakrit Bharti Sansthan Jaipur

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(d) Sequences and Progressions
It is only Trilokasāra which gives information about the dyadic type of sequences which pass through various types of finite and transfinite cardinals of sets.96
The fourteen types of sequences are as follows :
1. Sarva 2. Sama 3. Vişama 4. Kști 5. Akşti 6. Ghana 7. Aghana 8. Kști Mātīka 9. Aksti Mātýka 10. Ghana Mātặka
1, 2, 3, 4, 5, ....... 2, 4, 6, 8, 10, ............ 1, 3, 5, 7, 9, ........ 12, 22, 32, 42, 52, ... ... ... 2, 3, 5, 6, 7, ................ 13, 23, 33, 43, 53, ......... 2, 3, 5, 6, 7, 9, 10, ...... 1, 2, 3, ... ... upto . Vx+1, v*+ 2 ......, X. (13))), (23)}....... upto the last cubable number before y. y+1, y+2, y +3, y +4, ... ...; X.
11. Aghana Mātņkā
12. Dvirūpa Varga
1 2 2,
2 2 2,
3 2 2 , ...............
13. Dvirūpa Ghana
3.20 3.21 3.22 2 , 2 , 2 , ........
14. Dvirüpa Ghanaghana
32.20 2 ,
32.21 2 ,
32.22 2
.........
The Jaina School, in every one of its cosmographical sets, describes innumerable concentric rings of alternate continents and oceans, the diameter of each of the successive rings is double that of its predecessor ring. The diameter of the nth ring could be found to be 20-1, by assuming that of the first to be unity.97
96. Cf. Jaina, L. C., Divergent sequences locating transfinite sets in
Trilokasāra, I. J. H. S., Vol. 12, no. 1, May 1977, 55-75. 97. Cf. T. P. G., pp. 69-75. Areas could also be compared in various
details of the islands and oceans.
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