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 1. For all terms with we have the upper estimate This inequality is strict for every "n" ≥ "b" + 2. Changing the index of summation to "k" = "n" – "b" and using the formula for the infinite geometric series, we obtain Since there is no integer strictly between 0 and 1, we have reached a contradiction, and so "e" must be irrational. Q.E.D. Another proof can be obtained from the previous one by noting that and this inequality is equivalent to the assertion that "bx" < 1. This is impossible, of course, since "b" and "x" are natural