According to a basic theorem of transfinite set theory the set of irrational numbers is uncountable, while the set of rational numbers is countable. This is contradicted by the fact that any pair of irrational numbers is separated by at least one rational number. Hence, in the interval [0,1] there exist more rational numbers than irrational numbers.

A conservative irrational pseudo-rotation of the two-torus is semi-conjugate to the irrational rotation if and only if it has the property of bounded mean motion [1]. (Here ‘irrational pseudo-rotation’ means a toral homeomorphism with a unique and totally irrational rotation vector.) The aim of this note is to explore this concept some further. For instance, we provide an example which shows th...

Objective: This study is devoted to a relationship between irrational beliefs and severity of addiction in methadone treatment addicts in shahrood city, Iran. Method: the research was conducted between 56 addicts that was in treatment with methadone. They were selected with using Simple random sampling method then evaluated by Irrational Beliefs Test (IBT) and and severity of addiction Semi-str...

Social animals have to make collective decisions on a daily basis. In most instances, these decisions are taken by consensus, when the group does what the majority of individuals want. Individuals have to base these decisions on the information they perceive from their socioecological landscape. The perception mechanisms they use can influence the cost of collective decisions. Here I show that ...

Contrary to my critics, voter irrationality does not imply that economists cannot mitigate political failure. With rational voters, reform-minded economists have few viable tactics; with irrational voters reformers have more options. Rational voters can be swayed only by facts and logic; irrational voters could respond to better rhetoric. Rational voters strategically punish those who ignore th...

It remains unclear if patients with different types of common mental disorders, such as adjustment, anxiety and depressive disorders, have the same irrational ideas. The aim of this prospective cohort study (n = 190) is to investigate differences in level and type of irrational beliefs among these groups and to examine whether a change in irrational beliefs is related to symptom recovery. Irrat...