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 every
real 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.
