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
Irrational number Consider ; if this is rational, then take "a" = "b" = . Otherwise, take "a" to be the irrational number and "b" = . Then "a" = () = = = 2, which is rational. Although the above argument does not decide between the two cases, the Gelfond–Schneider theorem shows that is transcendental, hence irrational. This theorem states that if "a" and "b" are both algebraic numbers, and "a" is not equal to 0 or 1, and "b" is not a rational number, then any value of "a" is a transcendental number (there can be more than one value