Page:Philosophy and Fun of Algebra.djvu/86

PHILOSOPHY AND FUN OF ALGEBRA two ounces, it will be all eaten up when sixteen children have gone through the room. If the cake weighs only one pound, it will be eaten up when eight children have gone through the room. But if each child eats only one ounce, then again sixteen children will have to go through the room before the cake is eaten up, and so on. Many questions could be asked, all depending on the size of the cake and the size of each child's share.

All this time you are tied to an hypothesis that the children eat cake (more or less).

But now suppose we are freed from that hypothesis. Suppose no cake is given to the children. How many can pass through the room before it is all eaten up?

The answer to that is: "An infinite number." Infinity does not mean any particular number, or a very large number. It means a loosened chain, a discarded hypothesis; escape from the rule we were working under. Something else, not the size of the cake, determine the number of children. Infinity does not mean that there are enough children in the world now to go on 82