Irrational number
Elementary
An irrational number is a number that cannot be written as a fraction of whole numbers (or negative whole numbers).
High school
An irrational number is a real number that cannot be written as a fraction of integers.
Examples
Examples
- $\pi$ Elementary
- $e$ High school
-
$\sqrt{2}$
High school
$\sqrt{2}$ is irrational, because it is not a ratio of integers.
Properties
- The decimal expansion of an irrational number neither ends nor repeats.
- The irrational numbers are uncountable, while the rational numbers are countable.