Irrational numbers
Irrational numbers are real numbers that cannot be expressed as a finite decimal or fraction, having an infinite number of digits that never repeat in a predictable pattern. They play a crucial role in various areas of mathematics, including Algebra, Geometry, and Calculus. The discovery of irrational numbers is often attributed to the ancient Greek mathematician Hippasus of Metapontum, who is said to have proved that the square root of 2 is irrational. Irrational numbers are closely related to Transcendental numbers, which are numbers that are not the root of any polynomial equation with rational coefficients. The study of irrational numbers has led to important advancements in Number theory and has connections to other fields, such as Fractal geometry and Chaos theory.