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:
“Art is not to be taught in Academies. It is what one looks at, not what one listens to, that makes the artist. The real schools should be the streets.”
—Oscar Wilde (1854–1900)
“Michelangelo said to Pope Julius II, “Self negation is noble, self-culture is beneficent, self-possession is manly, but to the truly great and inspiring soul they are poor and tame compared to self-abuse.” Mr. Brown, here, in one of his latest and most graceful poems refers to it in an eloquent line which is destined to live to the end of time—”None know it but to love it, None name it but to praise.””
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)