Deshbhushanji Aacharya Abhinandan Granth

SR No.: 012045
Original Sutra Author: N/A
Author: R C Gupta
Publisher: Deshbhushanji Maharaj Trust
Publication Year: 1987
Total Pages: 1766
Language: Hindi, English
Classification: Smruti_Granth & Articles
File Size: 56 MB

Page 911

8400,000 maha latang =1 maha lata
maha lata =l shri kalpa
shri kalpa =1 haste prahelit » haste prahelit =1 achlatma
9.1. CLASSIFICATION OF NUMBERS
The introduction of such large numbers led the Jainas to the conception of infinity. The Jainas, like the Greece, do not consider 'unity' a number (Eko gananāsamkhyā na upeti). In Anuyogadwara-sutra(about 100 B.C.), the whole set of numbers is divided into three groups :
1. Sankhyeya ("numerable") 2. Asankhyeya ("in-numerable")
3. Ananta (infinite") and the highest numberable number is defined as :
"Consider a trough of the size of Jambudvipa, whose diameter is 100,000 Yojana and the circumference is 316227 Yojana, 3 gavyuti, 128 dhanu, 13 angula and a little over. Now fill up this trough with white mustard seeds counting them one after another. In the same manner fill up with mustard seeds other troughs of the sizes of the various lands and seas of the Jain Cosmography and count the seeds one after another. The total number of mustard seeds will still be less than the highest numerable number. Thus it is difficult to reach the highest number amongst the numerables. The highest numberable number of the carly Jainas corresponds to what is called Aleph Zero or Aleph-Null in modern mathematics."
Let N be the highest numerable number as defined above. For numbers beyond that, the Anuyogadwara-Sutra suggests the following sequence of operations :
2, 3,.......
................N, (N +1). (N+2),...........................[(N+1)-1], (N+1), (N+2),.........................((N+1)*--1), (N+1), (N+2)4,.........................((N+1)8-1], (N+1)", (N+2)...........................(N+1)16-11 (N+1)', (N+2),......................[(N+1)32–1], (N+1)32............
It may be observed here, that in the above classification of numbers there is an attempt to defin numbers beyond Aleph-Zero. The theory of such numbers was fully developed by George Canter in 1883. The fact that an attempt was made in India by the Jaina mathematicians to define such numbers in the 1st century of the Christian era is really commendable.
The Sthanana ga-Sutra: before (300 B.C.) gives the following interesting classification of infinity (ananta):
“Know that infinity is of five kinds, such as infinite in one direction, infinite in two directions, infinite in superficial expanse, infinite in all expanse, infinite in eternity."
1. See. Smith's History of Mathematics. Vol. II. P, 26. 2. See Sutra 146. 3. „ „ 462.
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