Going forward, K and K' will always denote two inertial frames of the same construction, with K' moving along the x-axis of K in the positive direction, at a constant velocity v ≠ 0. Since K and K' are both inertial frames, K is also moving relative to K' at some constant velocity v' ≠ 0. Both v and v' are finite, for the speed of every particle is finite.
Notes: (a) vectors are written in boldface, e.g. velocity v, while scalars in plain text, e.g. speed v = |v|, (b) we'll always assume that all inertial frames are of the same construction.