Warp 9 is the fastest attainable integer-designated warp speed. Warp 10 is infinite speed. Of course the writers for Star Trek were inconsistent and probably many had no ability to do math, which is why in some episodes there are ships going at warp 14 or warp 36.
https://www.ex-astris-scientia.org/treknology/warp6.htm
Warp 9 is the fastest attainable integer-designated warp speed. Warp 10 is infinite speed. Of course the writers for Star Trek were inconsistent and probably many had no ability to do math, which is why in some episodes there are ships going at warp 14 or warp 36.
That infinite warp episode was probably the worst episode of star trek of all.
Seriously, gets "infinite speed" and completes a week or two of conventional travel.
The books justified this by saying the warp chart was rewritten sometime between Kirk and Picard's eras.
In other words, warp 9 in Picard's era is a hell of a lot faster than warp 9 in Kirk's era.