Irrational exuberance Pink also used the phrase in 2009 in his book "" in the chapter discussing how extrinsic motivation can encourage short-term thinking at the cost of long-term health: "This is the nature of economic bubbles: What seems to be irrational exuberance is ultimately a bad case of extrinsically motivated myopia". Irrational exuberance "Irrational exuberance" is a phrase used by the then-Federal Reserve Board chairman, Alan Greenspan, in a speech given at the American Enterprise Institute during the dot-com bubble of the 1990s. The phrase was interpreted as a warning that the market might be overvalued. Greenspan's comment was made during
Proof that e is irrational a proof that "e" is not a root of a second degree polynomial with rational coefficients. This last fact implies that "e" is irrational. His proofs are similar to Fourier's proof of the irrationality of "e". In 1891, Hurwitz explained how it is possible to prove along the same line of ideas that "e" is not a root of a third degree polynomial with rational coefficients. In particular, "e" is irrational. More generally, "e" is irrational for any non-zero rational "q". Proof that e is irrational The number "e" was introduced by Jacob Bernoulli in 1683. More than half a