as title, 因为很多人还没有课本, 所以 po 出来跟大家分享. 0.11 Find the error in the following proof that all horses are the same color. CLAIM: In any set of h horses, all horses are the same color. PROOF: By induction on h. Basis: For h == 1. In any set containing just one horse, all horses clearly are the same color. Induction step: For k >= 1 assume that the claim is true for h == k and prove that it is true for h == k + 1. Take any set H of k + 1 horses. We show that all the horses in this set are the same color. Remove one horse from this set to obtain the set H[1] with just k horses. By the induction hypothesis, all the horses in H[1] are the same color. Now replace the removed horse and remove a different one to obtain the set H[2]. By the same argument, all the horses in H[2] are the same color. Therefore all the horses in H must be the same color, and the proof is complete. 0.12 Show that every graph with 2 or more nodes contains two nodes that have equal degrees. -- その乾いた哀愁の瞳に去来するものは何か？ 失ったもの 得たもの そして广大なネットの狭间で彼が见たものとは？ 虚像と实存と记号の中に彼は今、何を想うのか？ ＜バトルプログラマーシラセ＞ --

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