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
Irrational number then no integral power of it can be an integer, as in lowest terms there must be a prime in the denominator that does not divide into the numerator whatever power each is raised to. Therefore, if an integer is not an exact "k" power of another integer, then that first integer's "k" root is irrational. Perhaps the numbers most easy to prove irrational are certain logarithms. Here is a proof by contradiction that log 3 is irrational. Notice that log 3 ≈ 1.58 > 0. Assume log 3 is rational. For some positive integers "m" and "n", we have