What is Infinity (अनंत)?
Infinity, as we hear this word our brain instantaneously thinks of something very big and enormous which we can’t visualize. And indeed, infinity is limitless (अनंत). Mathematically, it is represented by the symbol ‘ꝏ’, sometimes called as a lemniscate.
If you open Mathematical Books of today, you will find the idea of infinity mentioned in somewhat higher level courses. You won’t, however, find either the infinite or the infinitesimal in an elementary book on algebra, let alone arithmetic! The only thing you may find in an algebra book is a very stern warning about not ever dividing by zero! (Because if you divide any number by zero, you get infinity).
On the other hand, in the algebra books of ancient times in India, we find both the infinite and the infinitesimal treated routinely. One such example is Bhaskaracharya Bijaganita (his book on Algebra) and Lilavati (his book on Arithmetic). Bhaskaracharya was a twelfth-century Indian mathematician and astronomer. He was born in Bijapur in Karnataka.
While Newton and Leibniz have been credited with differential and integral calculus, there is strong evidence to suggest that Bhaskaracharya was a pioneer in some of the principles of differential calculus.
Definition of Inifinity – Bhaskaracharya’s Bijaganita 2.18
In Bijaganita, we find the following shlok
Infinity further explained – Bhaskaracharya’s Bijaganita 2.20
For Khahara, he explicitly adds a colorful description
Mr. Avinash Sathaye, has explained this very well in his essay. The mathematical explanation follows as, we write ꝏ to denote the “khahara” i.e. 1/0.
The additional facts about “khahara” can be presented as,
X* ꝏ + Y = X* ꝏ, for any number X and Y. It states that when a “khahara” is added to an ordinary number, then only the “khahara” survives. This is the same as infinity just represented by another name.
In ancient Indian Mathematics, we find Jain texts discussing various such concepts of infinities. These texts are mainly religious or philosophical, but often carry a healthy amount of serious mathematics. They seem to introduce formal concepts of finite or enumerable, innumerable (very large but still finite) and infinite. They even classify multidimensional concepts for infinity.
In Lilavati (Shlok 48), Bhaskaracharya gives more instruction about multiplying by zero
Mention of Inifinity in Ishavasya Upanishad!
The invocatory verse of Ishavasya Upanishad which is part of Shukla Yajur Veda and it dates way back than Bhaskaracharya also talks about a rather precise concept of infinity. It goes something like this,
Infinity is a central concept as far as advanced sciences are concerned, such a great advancement at such complex subject shows how rich and prosperous was our culture. We hope you have understood infinity from both the modern as well as ancient perspective. Please let us know your thoughts on this and if anything you’d like to add.
Read our article on Top Shloks from Chanakya Neeti.