Q = {rational numbers}
= {irrational numbers}
Then
= R = {real numbers}
To represent a rational number on the number line
Mark the following rationals on the number line:

To represent an irrational number on the number line
To mark
, an irrational number, on the number line.
Then in rt.
= 1 + 1

Cut off OP = OB =
on the number line.
on the number line.


, if AO = 2 and AB = 1
Cut off OP = OB = 
on the number line.
In the same way
can be represented on the number line.
(i) For every real number, there is a corresponding point on the number line.
(ii) For every point on the number line, there exists a real number.![]()
with rational denominator.
![]()

with rational denominator.
![]()

