Predictably Irrational Predictably Irrational Predictably Irrational: The Hidden Forces That Shape Our Decisions is a 2008 book by Dan Ariely, in which he challenges readers' assumptions about making decisions based on rational thought. Ariely explains, "My goal, by the end of this book, is to help you fundamentally rethink what makes you and the people around you tick. I hope to lead you there by presenting a wide range of scientific experiments, findings, and anecdotes that are in many cases quite amusing. Once you see how systematic certain mistakes are—how we repeat them again and again—I think you will begin to learn
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