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,
Irrational number can never be expressed as a quotient of integers "m"/"n" with "n" ≠ 0. Cases such as log 2 can be treated similarly. Almost all irrational numbers are transcendental and all real transcendental numbers are irrational (there are also complex transcendental numbers): the article on transcendental numbers lists several examples. So "e" and π are irrational for all nonzero rational "r", and, e.g., "e" is irrational, too. Irrational numbers can also be found within the countable set of real algebraic numbers (essentially defined as the real roots of polynomials with integer coefficients), i.e., as real solutions of polynomial equations where