- See: Dirichlet Function, Repeating Decimal, Cantor's Diagonal Argument,
- (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/irrational_number Retrieved:2014-11-23.
- In mathematics, an irrational number is any real number that cannot be expressed as a ratio of integers. Informally, this means that an irrational number cannot be represented as a simple fraction. Irrational numbers are those real numbers that cannot be represented as terminating or repeating decimals. As a consequence of Cantor's proof that the real numbers are uncountable (and the rationals countable) it follows that almost all real numbers are irrational. When the ratio of lengths of two line segments is irrational, the line segments are also described as being incommensurable, meaning they share no measure in common. Perhaps the best-known irrational numbers are: the ratio of a circle's circumference to its diameter Pi, Euler's number e, the golden ratio φ, and the square root of two √.