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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 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 ...
The set of rational numbers includes all integers, which are fractions with a denominator of 1. The symbol of the rational numbers is . [19] Decimal fractions like 0.3 and 25.12 are a special type of rational numbers since
This category represents all rational numbers, that is, those real numbers which can be represented in the form: ...where and are integers and is ...
In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be rational numbers ; they may be taken in any field K .
In number theory, a cyclotomic field is a number field obtained by adjoining a complex root of unity to , the field of rational numbers. [ 1 ] Cyclotomic fields played a crucial role in the development of modern algebra and number theory because of their relation with Fermat's Last Theorem .
It is the ring of integers in the number field () of Gaussian rationals, consisting of complex numbers whose real and imaginary parts are rational numbers. Like the rational integers, [] is a Euclidean domain. The ring of integers of an algebraic number field is the unique maximal order in the field. It is always a Dedekind domain. [4]
The Avogadro constant, commonly denoted N A [1] or L, [2] is an SI defining constant with an exact value of 6.022 140 76 × 10 23 mol −1 (reciprocal moles). [3] [4] It is this defined number of constituent particles (usually molecules, atoms, ions, or ion pairs—in general, entities) per mole and used as a normalization factor in relating the amount of substance, n(X), in a sample of a ...