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The meaning of the word Kati is - how many? Here the numbers starting from two and increasing up to the largest numerate are all indicative of 'how many'.
The meaning of Akati is innumerate (finite, but uncountable) and infinite. The meaning of Avaktavya inexpressible) is the digit 'one'.
On the basis of the Uttaradhyayana and the Anuyogadvara aphorisms, it has been mentioned that the number 'one' has not been regarded as the calculation number. In the Jain canonical texts, the minimal calculation number has been recognised as two. Why? Its exposition is necessary, and that has been given in the pages after the discussion of Digamber tradition.
(ii) Digambara tradition: In the Digambara tradition, the word 'Kadi' occurs in place of the word Kati. Its meaning has been expressed as that of 'Kruti'. The mathematical exposition of the word Kruti is different from that in the Shvetambara tradition. Digambars, therefore, use another term 'Nokruti in their classification of numbers. Their three terms are:
Kruti • Nokruti • Avakatavya
Kruti
A number which fulfils following three criteria is termed as Kruti:
This increases after being squared, When the difference of its square and the number itself is greater than the number, When above difference is squared and proceeding number is subtracted again, result must be greater than the original number. This incremental pattern must continue as many times as this process is repeated.
Nokruti
The difference among these three terms can be understood with the help of examples. Let us take an example of number 'one':
There is no increase when it is squared(1)2= 1x1 = 1 When, out of this square the number itself is subtracted, it results in null - 1-1 = 0
There is no increase if the difference so obtained is squared again - 0 = 0 x 0 = 0 0-1 = not possible
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