The Number e

The number, e, is an irrational number defined as the limit of x as x approaches infinity of , with a decimal expansion beginning 2.7182818284590452353602874713527.... It is an important number in calculus, defined so that the slope of the line tangent to f(x) = e^x at (0, 1) is equal to 1.

Because f(x) = e^x has special calculus properties that simplify many calculations, it is considered the natural exponential function.