Irrationaalarvu

Irrationaalarvu is a mathematical term referring to numbers that cannot be expressed as a simple fraction. This means they cannot be written as a ratio of two integers, p/q, where q is not zero. Unlike rational numbers, which have terminating or repeating decimal representations, irrational numbers have decimal expansions that go on forever without any repeating pattern.

A well-known example of an irrational number is pi (π), which is approximately 3.14159. The decimal representation of pi continues infinitely without repetition. Another famous irrational number is the square root of 2 (√2), approximately 1.41421. The discovery of irrational numbers is attributed to the ancient Greeks, and it significantly impacted the development of mathematics, challenging existing geometric and arithmetic theories.

The set of irrational numbers, when combined with the set of rational numbers, forms the set of real numbers. While irrational numbers cannot be precisely expressed as fractions, their values can be approximated with increasing accuracy using rational numbers. Operations involving irrational numbers, such as addition, subtraction, multiplication, and division, can result in either rational or irrational numbers. For instance, the sum of an irrational number and a rational number is always irrational.