Irrational Man Irrational Man Irrational Man: A Study In Existential Philosophy is a 1958 book by the philosopher William Barrett, in which the author explains the philosophical background of existentialism and provides a discussion of several major existentialist thinkers, including Søren Kierkegaard, Friedrich Nietzsche, Martin Heidegger, and Jean-Paul Sartre. "Irrational Man" helped to introduce existentialism to the English-speaking world and has been identified as one of the most useful books that discuss the subject, but Barrett has also been criticized for endorsing irrationality and for giving a distorted and misleading account of Georg Wilhelm Friedrich Hegel. Barrett discusses existentialism and its background,
Proof that π is irrational enough and that the sequence of all "g" converges to 0. But a sequence of numbers greater than or equal to |"y"| cannot converge to 0. Since "f"(/4) = cos(/2) = 0, it follows from claim 3 that /16 is irrational and therefore that is irrational. On the other hand, since another consequence of Claim 3 is that, if "x" ∈ Q \ {0}, then tan "x" is irrational. Laczkovich's proof is really about the hypergeometric function. In fact, "f"("x") = "F"(k; −"x") and Gauss found a continued fraction expansion of the hypergeometric function using its functional equation. This allowed