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 the coefficients formula_7 are integers and formula_8. Any rational root of this polynomial equation must be of the form "r" /"s", where "r" is a divisor of "a" and "s" is a divisor of "a". If a real root formula_9 of a polynomial formula_10 is not among these finitely many possibilities, it must be an irrational algebraic number. An exemplary proof for the existence of such algebraic irrationals is by showing that "x" = (2 + 1) is an irrational root of a polynomial with integer coefficients: it satisfies ("x" − 1) = 2 and hence "x" − 2"x" −