In mathematics, the **real line**, or **real number line** is the line whose points are the real numbers. That is, the real line is the set **R** of all real numbers, viewed as a geometric space, namely the Euclidean space of dimension one. It can be thought of as a vector space (or affine space), a metric space, a topological space, a measure space, or a linear continuum.

Just like the set of real numbers, the real line is usually denoted by the symbol **R** (or alternatively, the letter “R” in blackboard bold). However, it is sometimes denoted **R**1 in order to emphasize its role as the first Euclidean space.

This article focuses on the aspects of **R** as a geometric space in topology, geometry, and real analysis. The real numbers also play an important role in algebra as a field, but in this context **R** is rarely referred to as a line. For more information on **R** in all of its guises, see real number.

Read more about Real Line: As A Linear Continuum, As A Metric Space, As A Topological Space, As A Vector Space, As A Measure Space

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