Just an FYI. In Star Trek at least the warp system works like this: warp-1 is the speed of light and it then increases exponentially with warp-10 being infinite velocity.
> it then increases exponentially with warp-10 being infinite velocity
No, no, no. That was only in the Voyager episode Threshold. It is widely regarded as one of the worst Voyager episodes, and the entire plot of that episode doesn't make any sense. There are questions of if this episode is even canon.
In any event, there are other Star Trek episodes where warp 10 is not a hard limit. All Good Things has ships traveling at Warp 13. The Kelvans modified the TOS Enterprise to travel at Warp 11. Even within Voyager, transwarp conduits allow for travel faster than whatever warp 10 would be if you disregard Threshold.
Warp 10 is not infinite velocity. It's just a line in a terribly written episode.
No, it is actually (mostly) correct. In ST:TNG they redefined the definition such that it is infinite. It was documented in the Star Trek: The Next Generation Technical Manual, which was published in 1991 and was written by the technical advisors for the series, who based it if the internal series technical bibles[1]. This was a distinct change from the original TOS which they never explained or formally retconned, but for all the series in that era it holds.
That was the standard scale used ST:TNG, ST:DS9, and ST:VOY with the notable exception of All Good Things. Obviously the point was to convey to the audience "Hey look, in the future things go much faster." Unfortunately they had originally chosen a scale that doesn't make that obvious to most viewers (it is not intuitively obvious that Warp 9.999 is substantially faster than Warp 9.99[2]). At a practical level it also very inconvenient to have a speed scale where all of the speeds share the same prefix (IOW, it is much easier for the captain to call out "Warp 9" and "Warp 12" then it is is to call out "Warp 9.99" and "Warp 9.999."
I choose to believe that the in the All Good Things timeline that once Federation started building ships that consistently exceeded 9.9 they came up with a modified scale that had better resolution and was easier to use, but that doesn't change the fact that Threshold (despite being terrible) is actually consistent with the existing source content and All Good Tings is not.
The TNG technical manual set warp 10 as infinite speed, and recalibrated the scale (so that warp 9 for the Enterprise-D was far faster than warp 9 of the original enterprise.
Presumably in the alternate future in AGT they had recalibrated the scale again (probably as warp 9.975 is a mouthful, 9.9954 would be a right pain)
Source: http://memory-alpha.wikia.com/wiki/Warp_factor