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 π is irrational enough and that the sequence of all "g" converges to 0. But a sequence of numbers greater than or equal to |"y"| cannot converge to 0. Since "f"(/4) = cos(/2) = 0, it follows from claim 3 that /16 is irrational and therefore that is irrational. On the other hand, since another consequence of Claim 3 is that, if "x" ∈ Q \ {0}, then tan "x" is irrational. Laczkovich's proof is really about the hypergeometric function. In fact, "f"("x") = "F"(k; −"x") and Gauss found a continued fraction expansion of the hypergeometric function using its functional equation. This allowed