Astraphobia immediately identified as a phobia because children naturally go through many fears as they mature. Their fear of thunder and lightning cannot be considered a fully developed phobia unless it persists for more than six months. In this case, the child's phobia should be addressed, for it may become a serious problem in adulthood. To lessen a child's fear during thunderstorms, the child can be distracted by games and activities. A bolder approach is to treat the storm as an entertainment; a fearless adult is an excellent role model for children. The most widely used and possibly the most effective
Proof that e is irrational between 2 and 3: We then analyze a blown-up difference "x" of the series representing "e" and its strictly smaller partial sum, which approximates the limiting value "e". By choosing the magnifying factor to be the factorial of "b", the fraction ⁄ and the partial sum are turned into integers, hence "x" must be a positive integer. However, the fast convergence of the series representation implies that the magnified approximation error "x" is still strictly smaller than 1. From this contradiction we deduce that "e" is irrational. Suppose that "e" is a rational number. Then there exist positive integers "a"