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Finite tree, infinite tree, root, rooted tree, leaf, finitely generated tree, path in a tree, fan theorem, arithmetic, Konig’s lemma.

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.

Arindama Singh¹

1. Department of Mathematics IIT Madras IT P.O., Chennai 600 036

Published

5 December 2017