In that theory an irrational number was the ratio of two incommensurable geometric magnitudes.
The widened idea is that even when a or x is an irrational number we may speak of a or x unit lengths by measure.
A number that cannot be expressed as the ratio of two whole numbers.
Note: The square roots of most whole numbers are irrational numbers.
mathematics
A real number which is not a rational number, i.e. it is not the ratio of two integers.
The decimal expansion of an irrational is infinite but does not end in an infinite repeating sequence of digits.
Examples of irrational numbers are pi, e and the square root of two.
(1995-04-12)