not algebraic. Examples include and . Trigonometric number: Any number that is the sine or cosine of a rational multiple of . Quadratic surd: A root of a quadratic equation with rational coefficients. 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. Algebraic integer: A root of a monic polynomial with integer coefficients. Non-standard numbers Transfinite numbers: Numbers that are greater than any natural number. Ordinal numbers: Finite and infinite numbers used to describe the order type of well-ordered sets. Cardinal numbers: Finite and infinite numbers used to describe the cardinalities of sets. Infinitesimals: These are smaller than any positive real number, but are nonetheless greater than zero. These were used in the initial development of calculus, and are used in synthetic differential geometry. Hyperreal numbers: The numbers used in non-standard analysis. These include infinite and infinitesimal numbers which possess certain properties of the real numbers. Surreal numbers: A number system that includes the hyperreal numbers as well as the ordinals. Computability and definability Computable number: A real number whose digits can be computed by some algorithm. Period: A number which can be computed as the integral of some algebraic function over an algebraic domain. Definable number: A real number that can be defined uniquely using a first-order formula with one free variable in the language of set theory. See also Almost integer Scalar (mathematics) References Mathematics-related lists Types