Irrational numbers are real numbers that are not rational numbers. They cannot be written as the ratio of two integers. If they are written as decimals, there are infinite digits after the decimal point, and they do not repeat. Common irrational numbers include square roots of non-perfect squares, π, and e (the latter two are transcendental numbers). Another characteristic of irrational numbers is the infinite continued fraction expression. According to legend, irrational numbers were first discovered by Hippos, a disciple of the Pythagorean school.

Irrational numbers are numbers that cannot be expressed as the ratio of two integers within the range of real numbers. Simply put, irrational numbers are infinite non-repeating decimals in the decimal system, such as pi, √2 (square root of 2), etc. Rational numbers are composed of all fractions and integers, and they can all be converted into finite decimals or infinite repeating decimals, such as 22/7, etc.