Encyclopedia

e,

e, in mathematics, irrational number occurring widely in mathematics and science, approximately equal to the value 2.71828; it is the base of natural, or Naperian, logarithms. The number e is defined as the limit of the expression (1+1/n)ⁿ as n becomes infinitely large, or

e =

lim n =>infinty

(1 + 1/n)n

In 1873 the French mathematician C. Hermite proved that e was transcendental, i.e., not a root of any algebraic equation; this proof constituted a great contribution to the growth of mathematics. The number e is also known as Euler's number, for Leonhard Euler, who discovered the famous formula e^iπ=-1, where i=, thus expressing the relationship between the numbers e, i, and π. The exponential function e^x, often written exp(x), occurs in various applications ranging from statistics to nuclear physics.

The Columbia Electronic Encyclopedia, 6th ed. Copyright © 2007, Columbia University Press. All rights reserved.

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