The Infinite Time Machine

The Infinite Time Machine?

I was watching The Big Bang Theory earlier on, the one with the time machine, and I got thinking. If you traveled back in time and then back to the present, picked up someone and went back to that some moment again, would you have two time machines? If so could you go and use it at the same time as the other? If the answer to this is yes, surely you could end up with an infinite amount of time machines? Or would this be some kind of paradox and be prevented from happening?