Irrational Man (1883-1891) Nietzsche's "most lyrical book" and "the expression of the loneliest Nietzsche." Finally, Barrett applies existentialist thought to the world of the late 1950s, during the Cold War. "Irrational Man" includes two appendices, "Negation, Finitude, and the Nature of Man", which reprints a 1957 paper by Barrett, and "Existence and Analytic Philosophers", a highly technical discussion of existentialism in relation to analytic philosophy. "Irrational Man" was first published in 1958 by Doubleday & Company, Inc. Later editions include those published by Greenwood Press, Inc. in 1977 and Anchor Books in 1990. "Irrational Man" received a positive review from Robert Jordan
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