[微積] 「有界數集必有最大元素」的反例故事
在Peter Lax所著的"Calculus with Applications"第14頁中,講了一個關於R. L. Moore的故事,引述如下:
The story is told that R. L. Moore, a famous mathematician in Texas, asked a student to give a proof or find a counterexample to the statement "Every bounded set of numbers has a largest element." The student came up with a counterexample: the set consisting of the numbers 1 and 2; it has a larger element, but no largest.
我不是很明白上文最後一句話。既然現在所考慮的集合為{1, 2},那當然是有界的,而其中2就是這集合裡的最大(largest)元素呀。那為何故事裡寫的是「較大(larger)」,而說並非「最大(largest)」?
不知是不是我英文太差,所以誤會了書本的意思,還請各位朋友指教,謝謝。
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