[gomaaa]

If you're travelling on a train moving at 99.9999% the speed of light and you get up and walk to the front of the train, didn't you just surpass the speed of light?

Wow! This post generated a LOT of responses! I don't have much to add except to say that your question is ALMOST EXACTLY the original problem that got Einstein thinking about the subject. Specifically, he asked what would happen if you were traveling in a train at a significant fraction of the speed of light and turned on a flashlight. The answer (as has already been described several times apparently) is that you can't simply add speeds when dealing with relativistic velocities. The math is more complicated.

[cripplecreek]

To me it seems to be a possible or impossible but unprovable in either situation.

At this point I guess travel to distant stars will come in the form of another method.