Ochlophobia going to sports games, or going to the mall. Ochlophobia Ochlophobia ("Fear of Crowds") and demophobia ("Fear of Unruly Mobs") are terms for types of social phobia or social anxiety disorder whose sufferers have a fear of crowds. Sufferers may offer various rationalizations of the phobia, such as the fear being trampled in a crowd, getting a deadly disease from people within the crowd, getting lost in the crowd, or feeling insignificant when surrounded by a crowd. People who are shy and introverted are most likely to experience ochlophobia, but not all introverts have anxiety problems. Ochlophobic people are often
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