Real Line (original) (raw)
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The term "real line" has a number of different meanings in mathematics.
Most commonly, "real line" is used to mean real axis, i.e., a line with a fixed scale so that everyreal number corresponds to a unique point on the line. The generalization of the real line to two dimensions is called the complex plane.
The term "real line" is also used to distinguish an ordinary line from a so-called imaginary line which can arise in algebraic geometry.
Renteln and Dundes (2005) give the following (bad) mathematical jokes about the real line:
Q: What is green and homeomorphic to the open unit interval? A: The real lime.
See also
Abscissa, Argand Diagram, Complex Plane, Imaginary Axis, Imaginary Line, Line,Moat-Crossing Problem, Real Axis Explore this topic in the MathWorld classroom
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References
Courant, R. and Robbins, H. What Is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed. Oxford, England: Oxford University Press, p. 57, 1996.Derbyshire, J. Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics. New York: Penguin, p. 178, 2004.Renteln, P. and Dundes, A. "Foolproof: A Sampling of Mathematical Folk Humor." Notices Amer. Math. Soc. 52, 24-34, 2005.
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Cite this as:
Weisstein, Eric W. "Real Line." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RealLine.html