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:
“We must have a real living determination to reach holiness. “I will be a saint” means I will despoil myself of all that is not God; I will strip my heart of all created things; I will live in poverty and detachment; I will renounce my will, my inclinations, my whims and fancies, and make myself a willing slave to the will of God.”
—Mother Teresa (b. 1910)
“Their bodies are buried in peace; but their name liveth for evermore.”
—Apocrypha. Ecclesiasticus, 44:14.
The line “their name liveth for evermore” was chosen by Rudyard Kipling on behalf of the Imperial War Graves Commission as an epitaph to be used in Commonwealth War Cemeteries. Kipling had himself lost a son in the fighting.