In mathematics, an irrational number is any real number that cannot be expressed as a ratio a/b, where a and b are integers and b is non-zero.
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 π, Euler's number e, the golden ratio φ, and the square root of two √2.
Read more about Irrational Number: History, Transcendental and Algebraic Irrationals, Decimal Expansions, Irrational Powers, Open Questions, The Set of All Irrationals, See Also
Famous quotes containing the words irrational and/or number:
“How did reason enter the world? As is fitting, in an irrational way, accidentally. We will have to guess at it, like a riddle.”
—Friedrich Nietzsche (1844–1900)
“You are the majority—in number and intelligence; therefore you are the force—which is justice. Some are scholars, others are owners; a glorious day will come when the scholars will be owners and the owners scholars. Then your power will be complete, and no man will protest against it.”
—Charles Baudelaire (1821–1867)