Fear of needles Fear of needles Fear of needles, known in medical literature as needle phobia, is the extreme fear of medical procedures involving injections or hypodermic needles. It is occasionally referred to as "aichmophobia" or "belonephobia", although these terms may also refer to a more general fear of sharply pointed objects. It has also been referred to as "trypanophobia", although the origin and proper usage of that term is highly controversial. The condition was officially recognized in 1994 in the DSM-IV (Diagnostic and Statistical Manual, 4th edition) as a specific phobia of blood/injection/injury type. Phobic level responses to injections cause sufferers to
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