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:
“People believe a man is in distress because his loved one dies in one day. But his real pain is less futile: it is that he finds out that sadness too does not last. Even pain has no meaning.”
—Albert Camus (1913–1960)
“There’s something like a line of gold thread running through a man’s words when he talks to his daughter, and gradually over the years it gets to be long enough for you pick up in your hands and weave into a cloth that feels like love itself. It’s another thing, though, to hold up that cloth for inspection.”
—John Gregory Brown (20th century)