The Traveling Spoonful

Two glasses sit on a table. One contains only water, and the other contains only wine. A full spoonful is taken from the wine glass, poured into the water glass, and stirred until the liquids are evenly mixed. Next, using the same spoon, a full spoonful of the water-and-wine mixture is transferred back into the wine glass. Assume that every spoonful has exactly the same volume and that nothing is spilled. After both transfers, which is greater: the amount of wine left in the water glass, or the amount of water carried into the wine glass?