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Real number. In mathematics, a real number is a number that can be used to measure a continuous one- dimensional quantity such as a distance, duration or temperature. Here, continuous means that pairs of values can have arbitrarily small differences.
In mathematics, computable numbers are the real numbers that can be computed to within any desired precision by a finite, terminating algorithm. They are also known as the recursive numbers, [ 1] effective numbers[ 2] or the computable reals[ 3] or recursive reals. [ 4] The concept of a computable real number was introduced by Émile Borel in ...
Complex number. A complex number can be visually represented as a pair of numbers (a, b) forming a vector on a diagram called an Argand diagram, representing the complex plane. Re is the real axis, Im is the imaginary axis, and i is the "imaginary unit", that satisfies i2 = −1. In mathematics, a complex number is an element of a number system ...
Surreal number. A visualization of the surreal number tree. In mathematics, the surreal number system is a totally ordered proper class containing not only the real numbers but also infinite and infinitesimal numbers, respectively larger or smaller in absolute value than any positive real number. Research on the Go endgame by John Horton Conway ...
In mathematics, de Moivre's formula (also known as de Moivre's theorem and de Moivre's identity) states that for any real number x and integer n it holds that. where i is the imaginary unit ( i2 = −1 ). The formula is named after Abraham de Moivre, although he never stated it in his works. [ 1] The expression cos x + i sin x is sometimes ...
Infinitesimal. In mathematics, an infinitesimal number is a non-zero quantity that is closer to 0 than any non-zero real number is. The word infinitesimal comes from a 17th-century Modern Latin coinage infinitesimus, which originally referred to the " infinity - eth " item in a sequence . Infinitesimals do not exist in the standard real number ...
An algebraic number is a number that is a root of a non-zero polynomial (of finite degree) in one variable with integer (or, equivalently, rational) coefficients. For example, the golden ratio, , is an algebraic number, because it is a root of the polynomial x2 − x − 1. That is, it is a value for x for which the polynomial evaluates to zero.
In mathematics, a ( real) interval is the set of all real numbers lying between two fixed endpoints with no "gaps". Each endpoint is either a real number or positive or negative infinity, indicating the interval extends without a bound. An interval can contain neither endpoint, either endpoint, or both endpoints.