Real number

In mathematics, the real numbers are intuitively defined as numbers that are in one-to-one correspondence with the points on an infinite line—the number line. The term "real number" is a retronym coined in response to "imaginary number".

History

Vulgar fractions had been used by the Egyptians around 1000 BC; around 500 BC, the Greek mathematicians led by Pythagoras realized the need for irrational numbers. Negative numbers were invented by Indian mathematicians around 600 AD, and then possibly reinvented in China shortly after. They were not used in Europe until the 1600s, but even in the late 1700s, Leonhard Euler discarded negative solutions to equations as unrealistic. The development of calculus in the 1700s used the entire set of real numbers without having defined them cleanly. The first rigorous definition was given by Georg Cantor in 1871.

Related Topics:
Vulgar fraction - Egyptians - 1000 BC - 500 BC - Greek - Pythagoras - Irrational number - Negative number - Indian - 600 - AD - China - 1600s - 1700s - Leonhard Euler - Calculus - 1700s - Georg Cantor - 1871

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