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 R1 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
Famous quotes containing the words real and/or line:
“Imaginary pains are by far the most real we suffer, since we feel a constant need for them and invent them because there is no way of doing without them.”
—E.M. Cioran (b. 1911)
“Expediency of literature, reason of literature, lawfulness of writing down a thought, is questioned; much is to say on both sides, and, while the fight waxes hot, thou, dearest scholar, stick to thy foolish task, add a line every hour, and between whiles add a line.”
—Ralph Waldo Emerson (1803–1882)