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### real line

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{{hatnote|This article covers advanced topics. For basic topics, see Number line.}}{{no footnotes|date=January 2013}}thumb|right|382x382px|The real lineIn 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 {{math|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 {{math|R}} (or alternatively, mathbb{R} , the letter â€œRâ€ in blackboard bold). However, it is sometimes denoted {{math|R1}} in order to emphasize its role as the first Euclidean space.This article focuses on the aspects of {{math|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 {{math|R}} is rarely referred to as a line. For more information on {{math|R}} in all of its guises, see real number.

## As a linear continuum

(File:Number line with x smaller than y.svg|thumb|300px|The order on the number line)(File:Illustration of supremum.svg|thumb|300px|Each set on the real number line has a supremum.)The real line is a linear continuum under the standard {{math|

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