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:
“Every age, every culture, every custom and tradition has its own character, its own weakness and its own strength, its beauties and cruelties; it accepts certain sufferings as matters of course, puts up patiently with certain evils. Human life is reduced to real suffering, to hell, only when two ages, two cultures and religions overlap.”
—Hermann Hesse (18771962)
“Experience has taught me, when I am shaving of a morning, to keep watch over my thoughts, because, if a line of poetry strays into my memory, my skin bristles so that the razor ceases to act.”
—A.E. (Alfred Edward)