Finite tree, infinite tree, root, rooted tree, leaf, finitely generated tree, path in a tree, fan theorem, arithmetic, Konig’s lemma.
Abstract
We present a ball game that can be continued as long as wewish. It looks as though the game would never end. But byapplying a result on trees, we show that the game nonethelessends in some finite number of moves. We then point out somedeep results on the natural number system connected withthe game.
