Infinite train?

[Forgind]

Imagine you're in a train. It's either a cycle or an infinitely long train extending in both directions. There is a number associated with each train car, and you are able to change that number. (You can change it to anything, but any train car might already have that value.) How can you figure out whether you're in an infinitely long train or a cycle?

Note that the train is not moving, you cannot change anything other than the number and which car you're in (moving forwards or backwards).