To understand what real numbers are, all you need to understand is the number line. Positive numbers to the right of zero and negative numbers to the left of zero. You will hear various complicated definitions of real numbers, but here's the simplest one. Any number that can be plotted on a number line is called a real number.
Let's look at a few examples. Say minus two. Yes! it can be plotted on the number line.
It's this point. So minus 2 is a real number. What about 0.5? Even though it's not an integer, it can be plotted on the number line. It will be somewhere here.
Now let's look at another number. Root 2, which is also called as square root of 2. If we calculate the value of root 2, we get it as 1.414 approximately. The digits after the decimal point do not end. These kind of numbers are called non-terminating decimal numbers. And yes, these numbers too can be plotted on the number line.
Plotting a non-terminating number might sound weird, but yes, it's possible. So root 2 is also a real number. And what about the special number pi. It approximately equals 3.14159.
Pi is also a non-terminating decimal number. And yes, it can be plotted on the number line, which makes it a real number. So that's our definition. Any number that can be plotted on a number line is called a real number. Now let's talk a bit about the different kinds of numbers we know.
The first kind is numbers with terminating decimals. Numbers like 0.375. The number stops at a point and does not go on and on. Then we have non-terminating recurring decimals.
Numbers like 0.6666 and so on. The sixes don't end. It's called recurring since the same number reoccurs and non-terminating since it reoccurs infinitely. And the third type is non-terminating. non-recurring decimals.
We just saw an example of this type. Root 2. It approximately equals 1.4142 and the digits after the decimal do not end. Hence it's called non-terminating.
It's called non-recurring since there is no specific pattern of re-occurrence. Broadly these are the three types of numbers we see in mathematics. Terminating, non-terminating recurring, and non-terminating non-recurring.
These two categories together are called rational numbers and the numbers in this category are called irrational numbers. These two categories together form real numbers. This is the other definition of real numbers. Rational numbers and irrational numbers together form real numbers. In the second part of this video, we will look at all categories real numbers comprise of.