Incompatibility between Einstein's Postulate and Special Theory of Relativity

A hyperbolic transformation relates relativistic velocities to corresponding Galilean velocity or rapidity. Comparison shows that usual definition of velocity is valid in Euclidian space but not valid in relativistic hyperbolic space. It also reveals that Einstein's postulate -- that the speed of light is the same in all inertial frames of reference -- is equivalent to the trivial statement that infinite velocity is the same in all inertial frames of reference. PACS: 03.30.+p