“Quiet!” the teacher said loudly and thumped the desk. “There’s nothing to laugh at. I will just explain what he means to say. For the division of bananas, we divided three by three, saying that each boy will get one banana. Similarly, we divided 1,000 by 1,000 to get one. What he is asking is that if zero banana is divided among zero, will each one get one? The answer is ‘no’. Mathematically, each will get an infinite number of bananas!”
Everyone laughed again. The boys understood the trick, arithmetic had played upon them. What they could not understand was why the teacher later complimented the boy who had asked that absurd question.
The boy had asked a question that had taken mathematicians several centuries to answer. Some mathematicians claimed that zero divided by zero was zero. Others claimed it to be unity. It was the Indian mathematician Bhaskara who proved that it is infinity. The boy who asked the intriguing question was Srinivasa Ramanujan. Throughout his life, whether in his native Kumbakonam or Cambridge, he was always ahead of his mathematics teachers.
The students laugh at the boy as they think it is a very silly question to ask: if no banana is distributed, then will everyone get one banana each. Although the boy's doubt was genuine and he did not ask it to stir up the class, his classmates do not understand the logic behind his doubt. But the teacher being an expert in the subject and well qualified, understands what he meant and explains it to the students.
The student had in fact understood what would happen when there is a specific number of items given and is asked to divide amongst a specific number of people. But he wants to know how one is supposed to divide when there is no particular number of bananas to divide. The teacher explains the concept of dividing the same number by itself. Any number divided by itself is one. For example, three divided by three would be \(1\), Thousand divided by thousand is 1. Similarly, zero divided by zero would give infinite options. It also works under the concept of probability. If one divides zero bananas, then each person stands a chance of receiving as many number of bananas as possible.
The symbol for Infinity
When the teacher explains this to the students, they understand the tricks that arithmetic has played on them. One might easily be tricked into thinking that when no banana is distributed, no one will receive the banana, but the fact is that it works on the chances of one receiving many bananas. But the boys being very young, did not understand the depth behind such a brilliant question. The question that the young boy asked was a huge concept that took a lot of Mathematicians to solve. The great Indian Mathematician Bhaskara was the one who solved and established that zero divided by zero is Infinity. The boy who had asked such a brilliant question was Srinivasa Ramanujan. All through his educational journey from his primary school in Kumbakonam to his days in Cambridge University, he was always ahead of his teachers.
Words with Difficult Meaning:
|Thumped||To hit at something really hard|
|Complimented||To appreciate someone for something good|
|Absurd||Having no logic|
|Intriguing||To stir interest|
State Council of Educational Research and Training (2019). Term-2 English Standard-9. From Zero to Infinity (pp. 81-93). Published by the Tamil Nadu Textbook and Educational Services Corporation.