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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 described as being incommensurable, meaning that they ...
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 ...
The golden ratio is an irrational number. Below are two short proofs of irrationality: Contradiction from an expression in lowest terms If φ were rational, then it would be the ratio of sides of a rectangle with integer sides (the rectangle comprising the entire diagram). But it would also be a ratio of integer sides of the smaller rectangle ...
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 number π appears in many formulae across mathematics and physics. It is an irrational number, meaning that it cannot be expressed exactly as a ratio of two integers, although fractions such as are commonly used to approximate it.
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
The English suffixes -phobia, -phobic, -phobe (from Greek φόβος phobos, "fear") occur in technical usage in psychiatry to construct words that describe irrational, abnormal, unwarranted, persistent, or disabling fear as a mental disorder (e.g. agoraphobia), in chemistry to describe chemical aversions (e.g. hydrophobic), in biology to describe organisms that dislike certain conditions (e.g ...
For rational numbers, ω(x, 1) = 0 and is at least 1 for irrational real numbers. A Liouville number is defined to have infinite measure of irrationality. Roth's theorem says that irrational real algebraic numbers have measure of irrationality 1. Measure of transcendence of a complex number