Prove that between any two rational numbers, there is an irrational number.
We will find an irrational number between two arbitrary rational numbers.
Answer: The proof is given below.
Follow the explanation given below.
We suppose a and b to be two rational numbers such that b > a. We claim c = a + (b - a)/√2 is an irrational number that lies between a and b.
0 < 1/√2 < 1
0 < 1/√2 (b - a) < (b - a)
a + 0 < a + 1/√2 (b - a) < a + (b - a)
a < a + (b - a)/√2 < b
This means c = a + (b - a)/√2 lies between a and b.