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 A stronger result is the following: Every rational number in the interval formula_23 can be written either as "a" for some irrational number "a" or as "n" for some natural number "n". Similarly, every positive rational number can be written either as formula_24 for some irrational number "a" or as formula_25 for some natural number "n". It is not known if formula_26 (or formula_27) is irrational. In fact, there is no pair of non-zero integers formula_28 for which it is known whether formula_29 is irrational. Moreover, it is not known whether or not the set formula_30 is algebraically independent over