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In mathematics, "rational" is often used as a noun abbreviating "rational number". The adjective rational sometimes means that the coefficients are rational numbers. For example, a rational point is a point with rational coordinates (i.e., a point whose coordinates are rational numbers); a rational matrix is a matrix of rational numbers; a rational polynomial may be a polynomial with rational ...
Such a number is algebraic and can be expressed as the sum of a rational number and the square root of a rational number. Constructible number: A number representing a length that can be constructed using a compass and straightedge. Constructible numbers form a subfield of the field of algebraic numbers, and include the quadratic surds.
Rational number arithmetic is the branch of arithmetic that deals with the manipulation of numbers that can be expressed as a ratio of two integers. [93] Most arithmetic operations on rational numbers can be calculated by performing a series of integer arithmetic operations on the numerators and the denominators of the involved numbers.
This category represents all rational numbers, that is, those real numbers which can be represented in the form: ...where and are integers and is ...
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 Stern–Brocot tree forms an infinite binary search tree with respect to the usual ordering of the rational numbers. [1] [2] The set of rational numbers descending from a node q is defined by the open interval (L q, H q) where L q is the ancestor of q that is smaller than q and closest to it in the tree (or L q = 0 if q has no smaller ...
The reciprocals of prime numbers have been of interest to mathematicians for various reasons. They do not have a finite sum, as Leonhard Euler proved in 1737.. Like rational numbers, the reciprocals of primes have repeating decimal representations.
The rational numbers in the open unit interval are an example. Another example is the set of dyadic rational numbers, the numbers that can be expressed as a fraction with an integer numerator and a power of two as the denominator. By Cantor's isomorphism theorem, the dyadic rational numbers are order-isomorphic to the whole set of rational numbers.