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Theorem: All horses have the same color. Proof: - Consider the statement "All horses in a set of n horses have the same color." - Basis Step: - Let n=1. Certainly, a set of one horse contains only horses of the same color. - Inductive Hypothesis: - Suppose that, for some kN, all horses in a set of k horses have the same color. - Inductive Step: - Let n=k+1, and let a set of k+1 horses be denoted H={h1,h2,,hk,hk+1}. - Two subsets of H are H1={h1,h2,,hk} and H2={h2,,hk,hk+1}, both of which have cardinality k. - By the hypothesis, all the horses in H1 have the same color and all the horses in H2 have the same color. Note that h2, for instance, is an element of both H1 and H2. - Then h2 is the same color as all the horses in H1 and all those in H2.h2 cannot be two different colors, thus, the color of all the horses in H1 and the color of all the horses in H2 must be the same color. - Thus, all the horses in H have the same color. - Therefore, by the Principle of Mathematical Induction, all horses have the same color. What is the error in this "proof