Irrationaalarv

Irrationaalarv is a Finnish term that translates to "irrational number" in English. Irrational numbers are real numbers that cannot be expressed as a simple fraction, meaning they cannot be written as a ratio of two integers, p/q, where p and q are integers and q is not zero. In contrast, rational numbers can be expressed in this form.

A key characteristic of irrational numbers is that their decimal representations are non-terminating and non-repeating. This means the digits after the decimal point go on forever without any discernible pattern or sequence of digits repeating.

Famous examples of irrational numbers include pi (π), which is approximately 3.14159..., and the square root of 2 (√2), which is approximately 1.41421.... Pi is the ratio of a circle's circumference to its diameter, and its decimal expansion continues infinitely without repetition. The square root of 2 is the length of the diagonal of a square with sides of length one, and it also has an infinite, non-repeating decimal representation.

The set of irrational numbers, when combined with the set of rational numbers, forms the set of all real numbers. While they cannot be precisely written as a fraction, irrational numbers are nonetheless essential in mathematics and physics for describing continuous quantities and relationships.