Irrational Exuberance (book) able to claim that he has foreseen any given crisis. Irrational Exuberance (book) Irrational Exuberance is a March 2000 book written by American economist Robert J. Shiller, a Yale University professor and 2013 Nobel Prize winner. The book examines economic bubbles in the 1990s and early 2000s, and is named after Federal Reserve Chairman Alan Greenspan's famed "irrational exuberance" quote warning of such a possible bubble in 1996. Published at the height of the dot-com boom, the text put forth several arguments demonstrating how the stock markets were overvalued at the time. The stock market collapse of 2000 happened the
Irrational number if complex number exponentiation is used). An example that provides a simple constructive proof is The base of the left side is irrational and the right side is rational, so one must prove that the exponent on the left side, formula_17, is irrational. This is so because, by the formula relating logarithms with different bases, which we can assume, for the sake of establishing a contradiction, equals a ratio "m/n" of positive integers. Then formula_19 hence formula_20 hence formula_21 hence formula_22, which is a contradictory pair of prime factorizations and hence violates the fundamental theorem of arithmetic (unique prime factorization).