1 Irrationality 3 1.1 Simple proofs of irrationality . . . . . . . . . . . . . . . . . . . . 3 1.2 Variation on a proof by Fourier (1815) . . . . . . . . . . . . . . . 10 1.2.1 Irrationality of e . . . . . . . . . . . . . . . . . . . . . . . 11 1.2.2 The number e is not quadratic . . . . . . . . . . . . . . . 11 1.2.3 Irrationality of e √ 2 (Following a suggestion of D.M. Masser) . . . . . . . ...

According to normative theories, reward-maximizing agents should have consistent preferences. Thus, when faced with alternatives A, B, and C, an individual preferring A to B and B to C should prefer A to C. However, it has been widely argued that humans can incur losses by violating this axiom of transitivity, despite strong evolutionary pressure for reward-maximizing choices. Here, adopting a ...

1 Irrationality 3 1.1 Simple proofs of irrationality . . . . . . . . . . . . . . . . . . . . 3 1.1.1 History of irrationality . . . . . . . . . . . . . . . . . . . . 10 1.2 Variation on a proof by Fourier (1815) . . . . . . . . . . . . . . . 12 1.2.1 Irrationality of e . . . . . . . . . . . . . . . . . . . . . . . 13 1.2.2 The number e is not quadratic . . . . . . . . . . . . . . . 13 1.2.3 Irr...

1 Irrationality 3 1.1 Simple proofs of irrationality . . . . . . . . . . . . . . . . . . . . 3 1.2 Variation on a proof by Fourier (1815) . . . . . . . . . . . . . . . 10 1.2.1 Irrationality of e . . . . . . . . . . . . . . . . . . . . . . . 11 1.2.2 The number e is not quadratic . . . . . . . . . . . . . . . 11 1.2.3 Irrationality of e √ 2 (Following a suggestion of D.M. Masser) . . . . . . . ...

Consensus forecasts are ine¢ cient. The weight placed on new information re‡ects the choices of the underlying individual forecasters— whose new information is noisier individually than in aggregate— so that the consensus forecast overweights older information. Using a cross-country panel of growth forecasts and new methodological insights, this paper …nds that: consensus forecasts are ine¢ cie...

w x Ž . In 1948, Paul Erdos E1 proved the irrationality of h 1 . Recently, ̋ 2 w x Peter Borwein used Pade approximation techniques B1 and some coḿ w x Ž . plex analysis methods B2 to prove the irrationality of both h 1 and q Ž . Ln 2 . Here we present a proof in the spirit of Apery’s magnificent proof ́ q Ž . w x of the irrationality of z 3 A , which was later delightfully accounted by w x Alf v...

1. Introduction. In his proof of the irrationality of ζ(3), Apéry [1] gave sequences of rational approximations to ζ(2) = π 2 /6 and to ζ(3) yielding the irrationality measures µ(ζ(2)) < 11.85078. .. and µ(ζ(3)) < 13.41782. .. Several improvements on such irrationality measures were subsequently given, and we refer to the introductions of the papers [3] and [4] for an account of these results. ...

Agents that interact with humans are known to benefit from integrating behavioral science and exploiting the fact that humans are irrational. Therefore, when designing agents for interacting with automated agents, it is crucial to know whether the other agents are acting irrationally and if so to what extent. However, little is known about whether irrationality is found in automated agent desig...

Most people strongly believe they are just, virtuous, and moral; yet regard the average person as distinctly less so. This invites accusations of irrationality in moral judgment and perception-but direct evidence of irrationality is absent. Here, we quantify this irrationality and compare it against the irrationality in other domains of positive self-evaluation. Participants (N = 270) judged th...