The Story of the Youth Who Went Forth to Learn What Fear Was undressed yourself to teach us fear.." as in figuratively "put something on, you've put yourself out to teach fear."). The Story of the Youth Who Went Forth to Learn What Fear Was "The Story of the Youth Who Went Forth to Learn What Fear Was" or "The Story of a Boy Who Went Forth to Learn Fear" () is a German folktale collected by the Brothers Grimm. It is tale number 4 in the collection. It was also included by Andrew Lang in "The Blue Fairy Book" (1889). The Grimms' first, 1812 edition contained a much shorter version, "Good Bowling
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