INTEREST AND EFFORT
is not only the last in time, but also settles the character of the entire game, and so gives meaning to all that has preceded. Nevertheless the earlier parts of the game are true parts of the game; they are not mere means for reaching a last inning.
In these illustrations we have seen how the last stage may be the fulfilling, the completing, or consummating of all that has gone before, and may thus decide the nature of the activity as a whole. In no case, however, is the end equivalent simply to an external result. The mere fact that one side won—the external result or object—is of no significance apart from the game whose conclusion it marks. Just so, we may say that the value of x in an algebraic equation is 5. But to say in general that x equals 5 is nonsense. This result is significant only as the outcome of a particular process of solving a particular equation. If, however, the mathematical inquiry is carried on to deal with other connected equations, it is possible to separate the result, 5, from what led up to it, and in further calculating to use 5 independently of the equation whose solu-
