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...

The tight junction is an intricate seal between adjoining epithelial cells that also separates the apical and basolateral membranes within these cells. A paper in this issue of Cell by Umeda et al. (2006) demonstrates that loss of the ZO scaffolding proteins prevents the formation of tight junctions but surprisingly does not perturb apico-basal polarity.