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real line

n. (context mathematics English) The real number system, viewed as a line.

Wikipedia
Real line

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 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 (or alternatively, R, the letter “ R” in blackboard bold). However, it is sometimes denoted in order to emphasize its role as the first Euclidean space.

This article focuses on the aspects of 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 is rarely referred to as a line. For more information on in all of its guises, see real number.

Usage examples of "real line".

At almost the same time, he realized what had been the real line, the line facing south, was liable not to hold, either.