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The mathematician, at first sight, may claim that he uses no other kind of logic than does his colleague in the law faculty. Yet as an illustration, let me recall his use of logic in the lemma that every sequence a of real num­ bers contains a monotonic subsequence, as taught in the beginner’ s course of analysis. The mathematician's logic says that

either for every n : there is an i>n : for every j > i : a ( i ) > a ( j ) or there is an n : for every i> n : there is a j > i : a ( i ) < a ( j ) .