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 fraction, "e" is irrational. A short proof of the previous equality is known. Since the simple continued fraction of "e" is not periodic, this also proves that "e" is not a root of second degree polynomial with rational coefficients; in particular, "e" is irrational. The most well-known proof is Joseph Fourier's proof by contradiction, which is based upon the equality Initially "e" is assumed to be a rational number of the form ⁄. Note that "b" could not be equal to 1 as "e" is not an integer. It can be shown using the above equality that "e" is strictly