# Special Relativity- Lorentz transformation

We know that in lorentz transformation , x'= lorentz factor*(x-vt) Suppose, that in unprimed frame , x=0 ; and the primed frame moves with velocity c wrt unprimed one. Then accor to the transformation, x'=-(infinite), as lorentz factor is infinite. But how can infinite distance be traversed by the primed frame with respect to the unprimed frame at a finite time?

First of all, the Lorentz transformation $x'=\gamma (x-vt)$ is not for distances, but for single events. Here $x'$ represents the position where some event occurs in the moving frame and approaches $\infty$. This isn't really possible because it would take an infinite amount of energy to accelerate an object with mass to $c$ which is why the $v=c$ frame does not exist.