The number e, also known as Euler's number, is a mathematical constant approximately equal to 2.71828 that can be characterized in many ways.

It is the base of natural logarithms.

It is the limit of (1 + 1/n)n as n approaches infinity, an expression that arises in the study of compound interest. It can also be calculated as the sum of the infinite series sum of 1/n!.

The (natural) exponential function f(x) = ex is the unique function f that equals its own derivative and satisfies the equation f(0) = 1; hence one can also define e as f(1).