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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" The following 15 pages are in this category, out of 15 ...
Download as PDF; Printable version; In other projects ... Pages in category "Rational numbers" The following 12 pages are in this category, out of 12 total.
For example, Metric Spaces by E. T. Copson uses the term boundary to refer to Hausdorff's border, which is defined as the intersection of a set with its boundary. [1] Hausdorff also introduced the term residue , which is defined as the intersection of a set with the closure of the border of its complement.
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.
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]
Rational numbers are defined as pairs of integers where the first number represents the numerator and the second number represents the denominator. For example, the pair (3, 7) represents the rational number . [153] One way to construct the real numbers relies on the concept of Dedekind cuts.
Download as PDF; Printable version; ... All rational numbers are algebraic numbers. ... Pages in category "Algebraic numbers" The following 19 pages are in this ...
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