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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 ...
Download as PDF; Printable version; ... Rational numbers (3 C, 12 P) Pages in category "Sets of real numbers"
Download as PDF; Printable version; In other projects Wikimedia Commons; Wikiversity; Wikidata item; ... This category represents all rational numbers, that is, ...
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.
Not all number systems can represent the same set of numbers; for example, Roman numerals cannot represent the number zero. Ideally, a numeral system will: Represent a useful set of numbers (e.g. all integers, or rational numbers) Give every number represented a unique representation (or at least a standard representation)
In the case of the rational numbers this means that any number has two irreducible fractions, related by a change of sign of both numerator and denominator; this ambiguity can be removed by requiring the denominator to be positive. In the case of rational functions the denominator could similarly be required to be a monic polynomial. [8]
Number theory began with the manipulation of numbers, that is, natural numbers (), and later expanded to integers and rational numbers (). Number theory was once called arithmetic, but nowadays this term is mostly used for numerical calculations. [15]
The set of rational numbers is not complete. For example, the sequence (1; 1.4; 1.41; 1.414; 1.4142; 1.41421; ...), where each term adds a digit of the decimal expansion of the positive square root of 2, is Cauchy but it does not converge to a rational number (in the real numbers, in contrast, it converges to the positive square root of 2).
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