It's easier to do this if we think about collision as a physical phenomenon rather than a mathematical abstraction. Two objects "touch" (which collision is just an amplification of,) when their atoms are close enough to exhibit electromagnetic repulsion of each other.

Therefore, the trains don't have to reach zero distance from one another...That front cowcatcher just has to be within, (I think, but I'm not sure, ) one atomic radius for the expected collision effects to occur. That's a finite distance, fuzzy, but >0. So just keep halving the distance, if that's what you wanna do, and you'll get within that radius.