We need to prove that Irrational numbers are dense in
Let, a and b be two real numbers, such that, a Since
And we are given that between any two real numbers there exist a rational number .
Therefore , let c in
Now , multiply by
Now, product of a rational and an irrational number is an irrational number , therefore , since c in
and a and b are real numbers and m is irrational number .
Therefore, we get that between any two real numbers a and b, with a Therefore, Irrational numbers are dense in real numbers .
Answer: Irrational numbers are dense in