CTK Insights

Mathematical induction fallacy "proves" that all rabbits are of the same color. Edward Barbeau quotes a computer science student who offered this refutation:

For the basis of induction pick any one rabbit. By default, the rabbit is of the same color with itself. For the inductive step, assume that any set of fewer than n + 1 rabbits have been proven to be monochromatic. Pick n + 1 rabbit. Temporarily remove one rabbit from the set, leaving a set, say A, of n rabbits. By the induction hypothesis,lemma,theorem,hypothesis,proposition, these n rabbits are of the same color. Put the "unused" rabbit back into the set and remove another one, leaving set B. As before, all rabbits in set B are of the same color. All the rabbits at hand (except for the special two) belong to both sets A and B, implying that the rabbits in both sets are of the same color. But the union A∪B contains all n + 1 rabbits which thus necessarily are all of the same color.

http://www.cut-the-knot.org/proofs/IntegerRabbits.shtml

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