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Irrational number. The number √ 2 is irrational. In mathematics, the irrational numbers ( in- + rational) are all the real numbers that are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two integers. When the ratio of lengths of two line segments is an irrational number, the line segments are also ...
π is an irrational number, meaning that it cannot be written as the ratio of two integers. Fractions such as 22 / 7 and 355 / 113 are commonly used to approximate π, but no common fraction (ratio of whole numbers) can be its exact value. [20]
A real number that is not rational is called irrational. [5] Irrational numbers include the square root of 2 ( ), π, e, and the golden ratio (φ). Since the set of rational numbers is countable, and the set of real numbers is uncountable, almost all real numbers are irrational. [1]
All rational numbers are real, but the converse is not true. Irrational numbers (): Real numbers that are not rational. Imaginary numbers: Numbers that equal the product of a real number and the imaginary unit , where =. The number 0 is both real and imaginary.
The golden ratio's negative −φ and reciprocal φ−1 are the two roots of the quadratic polynomial x2 + x − 1. The golden ratio is also an algebraic number and even an algebraic integer. It has minimal polynomial. This quadratic polynomial has two roots, and. The golden ratio is also closely related to the polynomial.
Wikimedia Commons has media related to Irrational numbers. In mathematics, an irrational number is any real number that is not a rational number, i.e., one that cannot be written as a fraction a / b with a and b integers and b not zero. This is also known as being incommensurable, or without common measure. The irrational numbers are precisely ...
In number theory, a Liouville number is a real number with the property that, for every positive integer , there exists a pair of integers with such that. The inequality implies that Liouville numbers possess an excellent sequence of rational number approximations. In 1844, Joseph Liouville proved a bound showing that there is a limit to how ...
Hippasus of Metapontum ( / ˈhɪpəsəs /; Greek: Ἵππασος ὁ Μεταποντῖνος, Híppasos; c. 530 – c. 450 BC) [1] was a Greek philosopher and early follower of Pythagoras. [2] [3] Little is known about his life or his beliefs, but he is sometimes credited with the discovery of the existence of irrational numbers. The ...