Addition to Lemma 81. In [1], § 4, there is a variant of the matrix formula (64) for the simple continued fraction of a real number. Given integers a0, a1, . . . with ai > 0 for i ≥ 1 and writing, for n ≥ 0, as usual, pn/qn = [a0, a1, . . . , an], one checks, by induction on n, the two formulae ( 1 a0 0 1 )( 1 0 a1 1 ) · · · ( 1 an 0 1 ) = ( pn−1 pn qn−1 qn ) if n is even ( 1 a0 0 1 )( 1 0 a1 1...

There are only aleph-zero rational numbers, while there 2 to the power real numbers. Hence probability that a randomly chosen number would be is 0. Yet proving rigorously any specific, natural, constant irrational usually very hard, witness still no proofs of irrationality Euler–Mascheroni constant, Catalan or \(\zeta (5)\). Inspired by Frits Beukers’ elegant rendition Apéry’s seminal (2)\) and...

Through a case study of Ghana’s TradeNet, a business-to-government (B2G) Electronic Data Interchange (EDI) implemented to automate and integrate customs clearance, this article investigates ‘irrationalities’ of IT-enabled change in the context of a developing country bureaucracy. Our data revealed that despite TradeNet’s potential for full automation and integration, bureaucrats sometimes prefe...

This study explores a phenomenon that has been shown to adversely affect managers' decisions—competitive irrationality. Managers are irrationally competitive in their decisions when they focus on damaging the profits of competitors, rather than improving their own profit performance Studies by Armstrong and Collopy (1996) and Griffith and Rust (1997) suggest that the phenoixiGnon is cominon but...