What? What? Where am I?

Yesterday after work I gave one of my students a lift back to the hotel where we are both staying.  Fifteen floors (well, fifteen that I can get to via stairs or elevator) and three elevators.  One of the obvious elevators only goes up to the ninth floor, but the others go up to fifteen.  I was amused and pleased when my student waited with me for the 1-15 elevator, saying she was on floor 10.  I'm on 14. 

So we get on, and program it for our floors.  The elevator stops and the mechanical voice states, "Ninth floor."  The door opens and I am facing a gentleman who says, "Going down?" 

"No, up."

He looks at me, obviously surprised.  Then he very gently but firmly (as if to a small child) says, "This is the ninth floor.  So you are going down."

"No, up!"  I point up to clarify.

The door closes on his puzzled face.