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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.
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 those numbers whose expansion in any given base (decimal ...
Irrational number. Square root of two; Quadratic irrational; Integer square root; Algebraic number. Pisot–Vijayaraghavan number; ... Pseudorandom number generator.
A repeating decimal or recurring decimal is a decimal representation of a number whose digits are eventually periodic (that is, after some place, the same sequence of digits is repeated forever); if this sequence consists only of zeros (that is if there is only a finite number of nonzero digits), the decimal is said to be terminating, and is not considered as repeating.
Any irrational number that is greater than one generates the Beatty sequence = {⌊ ⌋, ⌊ ⌋, ⌊ ⌋, …} The two irrational numbers and = / naturally satisfy the equation / + / =. The two Beatty sequences B r {\displaystyle {\mathcal {B}}_{r}} and B s {\displaystyle {\mathcal {B}}_{s}} that they generate form a pair of complementary ...
Some irrational numbers (as well as all the rationals) are the root of a polynomial with integer coefficients, such as the square root √2 = 1.414 ...
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Rational numbers have irrationality exponent 1, while (as a consequence of Dirichlet's approximation theorem) every irrational number has irrationality exponent at least 2. On the other hand, an application of Borel-Cantelli lemma shows that almost all numbers, including all algebraic irrational numbers , have an irrationality exponent exactly ...