1. INTRODUCTION. While there exist geometric proofs of irrationality for √2 [2], [27], no such proof for e, π , or ln 2 seems to be known. In section 2 we use a geometric construction to prove that e is irrational. The proof leads in section 3 to a new measure of irrationality for e, that is, a lower bound on the distance from e to a given rational number, as a function of its denominator. A co...

This yields an irrationality criterion (which is the basic tool for proving the irrationality of specific numbers), and Liouville extended it into a transcendence criterion. The proof by Liouville involves the irreducible polynomial f ∈ Z[X] of the given irrational algebraic number α. Since α is algebraic, there exists an irreducible polynomial f ∈ Z[X] such that f(α) = 0. Let d be the degree o...

This study examined the association among interpersonal relationships, irrational beliefs, and life satisfaction. Twenty-eight psychotherapy clients and 207 college undergraduates completed measures of interpersonal relations (Outcome Questionnaire; Lambert et al., 1996), irrationality (Rational Behavior Inventory; Shorkey & Whiteman, 1977), and life satisfaction (The Satisfaction with Life Sca...

Several new multiple-integral representations are proved for well-poised hypergeometric series and integrals. The results yield, in particular, transformations of the multiple integrals that cannot be achieved by evident changes of variable. All this generalizes some classical results of Whipple and Bailey in analysis and, on the other hand, certain analytic constructions with known connection ...

The Ratio-Bias phenomenon, observed by psychologist Seymour Epstein and colleagues, is a systematic manifestation of irrationality. When offered a choice between two lotteries, individuals consistently choose the lottery with the greater number of potential successes, even when it offers a smaller probability of success. In the current study, we conduct experiments to confirm this phenomenon an...

Economic models of animal behaviour assume that decision-makers are rational, meaning that they assess options according to intrinsic fitness value and not by comparison with available alternatives. This expectation is frequently violated, but the significance of irrational behaviour remains controversial. One possibility is that irrationality arises from cognitive constraints that necessitate ...

The present paper proposes an integrative account of social forms of practical irrationality and corresponding disruptions of individual and group-level emotion regulation (ER). I will especially focus on disruptions in ER by means of collaborative agential and doxastic akrasia. I begin by distinguishing mutual, communal and collaborative forms of akrasia. Such a taxonomy seems all the more nee...

The traditional economics and queueing literature typically assume that customers are fully rational. In contrast, in this paper, we study canonical service models with boundedly rational customers. We capture bounded rationality using a framework in which better decisions are made more often, while the best decision needs not always be made. We investigate the impact of bounded rationality on ...