Question

Prove that between any two different real numbers there is a rational number and an irrational number

Answer 1

Rational Number is the combination of both rational and irrational number.

Thus, any two real number it can be rational and an irrational number..

Example: -3.12 is a real number but it is also rational

and 8.3333.... is also a real number but it is also an irrational number.

Further,

Rational Number is the number in the form
`(p)/(q)`, where q≠0.

Example:
`(2)/(9), (-1)/(267), (875)/(2), 3, etc.`

Real Number is the all numbers including natural, whole, integers, rational, irrational number except the imaginary numbers.

Example:
`(548)/(5)`, 5, √28, etc.

The decimal which is non-terminating, non-repeating decimal expansion and thus it can't be written in the form of simple fraction is called irrational number.

Example: √5, π, 27.458978445...., etc.