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:
“There must be real gods
see, the painted gods
how fair!”
—Hilda Doolittle (1886–1961)
“The modern picture of The Artist began to form: The poor, but free spirit, plebeian but aspiring only to be classless, to cut himself forever free from the bonds of the greedy bourgeoisie, to be whatever the fat burghers feared most, to cross the line wherever they drew it, to look at the world in a way they couldn’t see, to be high, live low, stay young forever—in short, to be the bohemian.”
—Tom Wolfe (b. 1931)