课程名称︰分析导论优二
课程性质︰数学系大二必修
课程教师︰王振男
开课学院：理学院
开课系所︰数学系
考试日期（年月日）︰2015/04/28
考试时限（分钟）：25
试题 :
1
1. (10%) Is the set of irrationals in |R a G set?
δ
2. (10%) Find the fallacy in the following proof of showing the set of
∞
rationals, Q, is a G set. Let us enumerate Q = {q } . Choose n ∈ |N and
δ k k=1
1 1
define O = ∪ (q -─, q +─). It is clear that O is open. Next we observe
n k k n k n n
1 1
that (q -─, q +─) → {q } as n → ∞. Therefore, Q = ∩ O and so Q is a
k n k n k n n
G set.
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