This was the quote...

"A plane is standing on runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in opposite direction).

The question is:

Will the plane take off or not? Will it be able to run up and take off?"

It clearly says that the Plane MOVES in one direction. Even if it didn't, the jet or props move the plane, not the wheels. The guy who talked about friction in the wheel bearings had a point and there would be a certain amount of attraction or stickyness of the tires to the belt (surface tension), but as they spin faster and faster, they would over come that attraction to each other as they expand from centrifugal force (drag tires increase their diameter as the car launches) and push the plane away from the belt. Aside from all that BS... The whole point is that the tires don't drive the plane (we must assume becasue they DIDN'T say that the plane has no jets or props and was tire driven) and the belt has no real affect on how a plane functions, nor does a static runway.

The runway belt that advances at the plane represents a frictionless surface for the tires to sit on. A ice covered runway, or a lake (tons of friction really and more of a problem than a runway belt matching the attempted speed of a plane) could be substituted in your mind to help you realize how rediculous this is.

My final answer is Yes, the plane will be able to run up and take off, even if the belt is going twice as fast as the plane in the opposite direction. Oh no I didn't.