Aichmophobia Aichmophobia Aichmophobia () is a kind of specific phobia, the morbid fear of sharp things, such as pencils, needles, knives, a pointing finger, or even the sharp end of an umbrella and different sorts of protruding corners or sharp edges in furnitures and building constructions/materials. It is derived from the Greek "aichmē" (point) and "phobos" (fear). This fear may also be referred to as belonephobia or enetophobia. Sometimes this general term is used to refer to what is more specifically called fear of needles, or needle phobia. Fear of needles is the extreme and irrational fear of medical procedures involving
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"