Scientific Secrets of Jainism

Author(s): Nandighoshvijay
Publisher: Research Institute of Scientific Secrets from Indian Oriental Scriptures Ahmedabad

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Scientific Secrets of Jainism
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4. The sum of two natural numbers is always in the form of a different natural number. ( Zero is not regarded as a natural number because counting always begins with 1 and never with zero.) The modern mathematics expresses this thus -- "The set of natural numbers is closed with respect to a d d Ition
The concepts of addition of natural numbers was later symbolised as + And that was the first arithmetical operation on them. It has the noteworthy property that the sum of two natural numbers is also a natural number greater than each of the two natural number.
At initial stages the concept of subtraction implied the removal of smaller natural number from the bigger ones. The reverse could not be conceived of for a long time. But some one appears to have hit upon the idea of proceeding the other way round. He showed this with a practical example. Suppose a man has five coins of his own and he has to pay seven coins to some one else. He can pay seven coins to other person only after taking a loan of two coins from a third person. Thus 5 - 7 = -2, Here 5 stands for the number of coins that the man possesses as his own. - 7 stands for the number of coins that he has to pay to someone as a loan. - 2 stands for the number of coins
e man takes as a loan from the third person. Thus the negative (- ve) numbers denote debt. In short, the new process of subtracting a big number from a small number produced a category of negative (-ve) numbers. Compared to the natural numbers, they were unreal and imaginary. They were denoted by putting the negative (-ve) sign before natural numbers. These imaginary integers in the form of negative natural numbers came to be recognized as a set of negative integers and the real natural numbers in the form of positive numbers along with zero came to be recognised as a set of positive integers. These numbers can be arranged in an ascending order as under:
(......-1000.......-900........-100,....-90.......-50........-10......-9....-7........ 4,.....-1 ...0,...... 1.............9,..... 10,......60,...... 100,.....1000,..........)
Natural numbers are also called positive (+ve) integers.
A very important point emerges from the similarity of positive and negative integers. Every number on the right in the sequence is 1 more than the immediately preceding left one."