I know what you and Zeno are saying, I did last night too but wasn't thinking about that specificly.
The problem I have with Zeno's paradox is that his logic and illustrations are misleading to the point of being wrong.
You will never get to the otherside because according to the fractioning of the distance, time is also fractioned at the same rate and the time needed to cross never comes to completion,(in a vacuum).
I think what actually happens is that those units are a mental construct; perceived. I also think time is relative to the observer. So long as the person crossing the room intends on it he never does according to the shrinking units of measurement, yet when he percieves that he does, he actually does, and the parallel dimension where he doesn't ever cross ceases to exist at the moment that he percieves a reality where he does,(and he does).
edit- in other words, because he is racing against time and space, it require more energy then the time and space require at any one of the points, so at the point where he percieves that he touches the wall, the extra energy given by that perception allows him to break that percieved time/space barrier and he actually touches the other side and at the same moment he ceases to intend on reaching it which weakens the barrier and the never ending trajectory dependant on the intention ceases to exist.
By that way, a person could percieve that he or she had reached the end of the room at the half way point, at which point they would disappear and reappear at the otherside.
Is that a paradox?