epärationaaliluku

Epärationaaliluku is a Finnish term that translates to irrational number. An irrational number is a real number that cannot be expressed as a simple fraction, meaning it cannot be written in the form p/q, where p and q are integers and q is not zero. Unlike rational numbers, whose decimal representations either terminate or repeat, irrational numbers have decimal expansions that are non-terminating and non-repeating.

Perhaps the most famous example of an irrational number is pi (π), the ratio of a circle's circumference to its diameter. Its decimal expansion begins 3.1415926535... and continues infinitely without any repeating pattern. Another well-known irrational number is the square root of 2 (√2), which is approximately 1.4142135623... This number arises from the Pythagorean theorem, representing the length of the diagonal of a square with sides of length one.

Other examples of irrational numbers include the base of the natural logarithm, e, and the golden ratio, φ. The set of all irrational numbers, when combined with the set of all rational numbers, forms the set of real numbers. The existence of irrational numbers was a significant discovery in ancient Greek mathematics, challenging earlier beliefs that all quantities could be expressed as ratios of whole numbers.