the natural constant e is lim(1+1/x)^x, x→+∞ or lim(1+z)^(1/z), z→0. its value is approximately 2.71828, which is an infinite non-cyclic number.

e, as a mathematical constant, is the base of the natural logarithm function. it is sometimes called the euler number, named after the swiss mathematician euler; it also has the less common name napier's constant, in honor of the scottish mathematician john napier who introduced logarithms. like pi and the imaginary unit i, e is one of the most important constants in mathematics.