1.1 Introduction [5m]
I hope you took the quiz. Congratulations if you got the correct answer. In fact, I am 100% sure that you got the right answer. I have an idea that seems like fun. In the discussion board below, why don't you right down the reason for choosing your answer. Let's see if others came up with reasons different from yours. Also, you can read reasons given by others too.
This chapter is about "NUMBERS". And, it is impossible to think about NUMBERS without feeling proud of the immense contribution that Indian culture and Indian scholars have made to Arithmetic. Even the digits 0, 1, 2, ..., 9 that the World uses today are called the Hindu-Arabic numerals. Aryabhatta, Brahmagupta, Bhaskara, and Mahavira are commonly known classical mathematicians born in India.
In modern mathematics, Number Theory, is the branch that studies Integers. Srinivasa Ramanujan was one of the most respected number theorists in the World. His biography was rightly titled, "The Man Who Knew Infinity". On his birthday, 22nd December, India celebrates the National Mathematics Day. Another accomplished number theorist who has Indian roots, but born in Canada, is Manjul Bhargava. He was awarded the Fields medal in 2014, one of the highest awards for mathematicians.
The reason I am telling you this is because I do not want you to take numbers lightly. Numbers have the power to transform the world and make legends. But, for that, you need to understand them.
German mathematician Carl Friedrich Gauss said,
"Mathematics is the queen of the sciences—and number theory is the queen of mathematics."
This photograph shows a street in Old Delhi during normal business hours. One word that describes it is - crowded. If we wanted to express this more scientifically, we would say that the population density of Old Delhi is very high. Even sets of numbers have density. Which of these sets of numbers is most dense?
- Natural numbers
- Whole numbers
In this chapter, you will come across three interesting and beautiful aspects of numbers.
Can you imagine a number whose exact value in not known? What if I told you that there are more numbers whose exact value is not known compared to numbers whose exact value is known? In fact, if you choose any two numbers, no matter how close to each other, you can find infinitely many numbers between them whose exact value is not known? But, wait. Even more interesting is the fact that even though we do not know the exact value of some numbers, we can locate them precisely on a number line.
These numbers will be called irrational numbers. And, together with all the numbers you know so far (integers, and fractions), these numbers will form a large universe of numbers called the REAL NUMBERS. Most of the mathematics that you will study over the next four years will involve REAL NUMBERS. So, you better make friends with them.
So, let us begin....the journey to discover some new numbers, make some new friends, and play with them.