问题 单项选择题

If S is an infinite set of real numbers, is there a number in S that is less than every other number in S ?()
(1)Every number in S is an integer.
(2)Every number in S is positive.

A.条件(1)充分,但条件(2)不充分.

B.条件(2)充分,但条件(1)不充分.

C.条件(1)和(2)单独都不充分,但条件(1)和条件(2)联合起来充分.

D.条件(1)充分,条件(2)也充分.

E.条件(1)和条件(2)单独都不充分,条件(1)和条件(2)联合起来也不充分.

答案

参考答案:C

解析:

该题也即让考生求集合S中存在最小元素的充分条件。(1)不充分,因为S中的数可以为正整数,也可以为负整数,所以集合S中不存在最小值;(2)也不充分,因为最小的正数也是不存在的;(1)+(2)充分,因为此时集合S是一个所有正整数的集合,而最小的正整数为1。

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单项选择题