Irrational Numbers
A number ‘s’ is called irrational, if it cannot be written in the form p/q, where p and q are integers and q ≠ 0.
You already know that there are infinitely many rational numbers. It turns out that there are infinitely many irrational numbers too.
Some examples are:- √2, √3, √15, , 0.10110111011110...
Real Numbers
Remember the bag of rational numbers in previous video. If we now put all irrational numbers into the bag, will there be any number left on the number line? The answer is no! It turns out that the collection of all rational numbers and irrational numbers together make up what we call the collection of real numbers.
which is denoted by R.
Therefore, a real number is either rational or irrational. So, we can say that every real number is represented by a unique point on the number line. Also, every point on the number line represents a unique real number. This is why we call the number line, the real number line.
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