Another way in which the mysterious e arises is through the sum of the reciprocals of the factorials, and this gives a way of calculating e to a high degree of accuracy as this series converges rapidly because its terms approach zero very quickly indeed:
The real and the imaginary
Therstve chapters of this Very Short Introduction dealt mainly with positive integers. We emphasized factorization properties of integers, which led us to consider numbers that have no proper factorizations, which are the primes, a set that occupies a pivotal position in modern cryptography. We also looked at particular types of numbers, such as the Mersenne primes, which are intimately connected with perfect numbers and took time to introduce some special classes of integers that are important in counting certain naturally occurring collections. Throughout all this, the backdrop was the system of integers, which are the counting numbers, positive, negative, and zero.