 # Real number

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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 values can have arbitrarily small variations.[lower-alpha 1] Every real number can be almost uniquely represented by an infinite decimal expansion.[lower-alpha 2]

The real numbers are fundamental in calculus (and more generally in all mathematics), in particular by their role in the classical definitions of limits, continuity and derivatives.[lower-alpha 3]

The set of real numbers is denoted R or $\mathbb {R}$ and is sometimes called "the reals". The adjective real, used in the 17th century by René Descartes, distinguishes real numbers from imaginary numbers such as the square roots of −1.

The real numbers include the rational numbers, such as the integer −5 and the fraction 4/3. The rest of the real numbers are called irrational numbers, and include algebraic numbers (such as the square root 2 = 1.414...) and transcendental numbers (such as π = 3.1415...).

Real numbers can be thought of as all points on an infinitely long line called the number line or real line, where the points corresponding to integers (..., −2, −1, 0, 1, 2, ...) are equally spaced.