The positive, irrational (proved by Euler, 1737), transcendental (proved by Hermite, 1873) number which is the limit as n tends to infinity of
approximately 2.718 281 828 459 045 235 36…
According to Cajori, the first mathematician to call this number e was Leonard Euler, in manuscripts dated 1728 or 1729, a letter of 1731, and then in a publication of 1736.¹
e is the base of natural logarithms, so ln e = 1.
In calculus, ex is its own derivative.
(! is the factorial sign, indicating the product of all the integers greater than zero up to the one marked, so for example 5! = 1×2×3×4×5 = 120.)
1. Leonard Euler.
Mechanica sive motus scientia analytice exposita.
St. Petersburg, 1736.
Pages 251, 256.
e. The Story of a Number.
Princeton, NJ: Princeton University Press, 1994.
Copyright © 2000 Sizes, Inc. All rights reserved.
Last revised: 22 October 2002.