Questions tagged [eulers-number]

The mathematical constant e (wikipedia) can be defined in various equivalent ways:

• the unique positive real number such that the derivative of the function f(x) = ex is always equal to ex
• the unique positive real number such that the derivative of the function loge x = 1 / x
• the limit as n tends to infinity of (1 + 1/n) ^ n
• the sum of the infinite series 1 / n! as n goes from zero to infinity

Ths first of these accounts for the frequency with which e crops up in models involving compounded growth.