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The long real line pastes together ℵ 1 * + ℵ 1 copies of the real line plus a single point (here ℵ 1 * denotes the reversed ordering of ℵ 1) to create an ordered set that is "locally" identical to the real numbers, but somehow longer; for instance, there is an order-preserving embedding of ℵ 1 in the long real line but not in the real ...
Simple English; Slovenščina; ... the number line is usually called the real line or real number line, and is a geometric line isomorphic to the set of real numbers, ...
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In mathematics, the real numbers are intuitively defined as numbers that are in one-to-one correspondence with the points on an infinite line—the number line. The term "real number" is a retronym coined in response to "imaginary number". Together with the p-adic numbers, the reals are a limit set of the rational numbers. Real numbers may be ...
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.
A point on number line corresponds to a real number and vice versa. [15] Usually, integers are evenly spaced on the line, with positive numbers are on the right, negative numbers on the left. As an extension to the concept, an imaginary line representing imaginary numbers can be drawn perpendicular to the number line at zero. [16]
Date/Time Thumbnail Dimensions User Comment; current: 23:56, 29 November 2018: 689 × 225 (18 KB): Mikus: The line continues indefinitely in the positive and negative directions according to the rules of geometry which define a line without endpoints as an infinite line, a line with one endpoint as a ray, and a line with two endpoints as a line segment.
3. is the generalized number that is added to the real line to form the projectively extended real line. (fraktur 𝔠) denotes the cardinality of the continuum, which is the cardinality of the set of real numbers.