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一天,某城里一位理发师写下告示:我给本城里所有不给自己理发的人理发,而且只给这些人理发。可是,按照告示中所宣称的,则这位理发师的头发既不能由他自己来理,也不能由其他任何人来理,那么应该由谁来理呢?这就是著名的“罗素悖论”。克莱因(C.F.Klein)是德国著名数学家,格丁根学派的创始人之一。他上了年纪之后,在格丁根的地位如同神一般。格丁根流行一个笑话,说格丁根有两种教学家,一种教学家做他们自己要做但不是克莱因要他们做的事(给自己理发);另一类数学家儆克莱因要做但不是他们自己要做的事(由理发师理发)。这样克莱因不属于第一类,也不属于第二类,于是克莱因不是数学家(谁来给他理发)。
One day a barber in a town wrote down a note: I gave a haircut to all those in my town who did not give myself a hairdressing, and only gave them haircuts. However, according to the notice, the hairdresser’s hair can not be handled by himself or anyone else. Who should manage this? This is the famous Russell Paradox ". C. Klein is one of the founders of the famous German mathematician and Gerdingen school. After he was old, he had the same status as God in Gedingen. One of the most popular jokes in Goettingen is that Gerdingen has two kinds of pedagogues, a kind of pedagogue who do what they themselves want to do but not what Klein wants them to do (to herself); another mathematician, Things to do but not what they want to do (haircut by barber). So Klein does not belong to the first category, does not belong to the second category, so Klein is not a mathematician (who will give him a haircut).