The mathematical constant e is the unique real number such that the value of the derivative (slope of the tangent line) of the function f(x) = e at the point x = 0 is exactly 1. The function e so defined is called the exponential function, and its inverse is the natural logarithm, or logarithm to base e. The number e is also commonly defined as the base of the natural logarithm (using an integral to define the latter), as the limit of a certain s...
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The mathematical constant e is the unique real number such that the value of the derivative (slope of the tangent line) of the function f(x) = e at the point x = 0 is exactly 1. The function e so defined is called the exponential function, and its inverse is the natural logarithm, or logarithm to base e. The number e is also commonly defined as the base of the natural logarithm (using an integral to define the latter), as the limit of a certain sequence, or as the sum of a certain series (see the alternative characterizations, below).
e is one of the most important numbers in mathematics, alongside the additive and multiplicative identities 0 and 1, the constant π, and the imaginary unit i. (These are the five constants appearing in one formulation of Euler's identity.)
The number e is sometimes called Euler's number after the Swiss mathematician Leonhard Euler. (e is not to be confused with γ – the Euler–Mascheroni constant, sometimes called simply Euler's constant.)
The number e is...
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