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,
Quadratic irrational number which this is true, hence the smallest number for which "q" is also an integer. Then: is also an integer. But 0 < ( − "n") < 1 so ( − "n")"q" < "q". Hence ( − "n")"q" is an integer smaller than "q". This is a contradiction since "q" was defined to be the smallest number with this property; hence cannot be rational. Quadratic irrational number In mathematics, a quadratic irrational number (also known as a quadratic irrational, a quadratic irrationality or quadratic surd) is an irrational number that is the solution to some quadratic equation with rational coefficients