Hyperbolic numbers as Einstein numbers

In the special theory of relativity (SR) it is usual to highlight so-called paradoxes. One of these paradoxes is the formal appearance of speed values grater then the light speed. In this paper we show that most of these paradoxes arise due to the incompleteness of relativistic calculus over velocities. Namely, operation over speeds form a group by composition. In this case, the extension to the field is usually carried out using non-relativistic operations. © Published under licence by IOP Publishing Ltd.