課程名稱︰分析導論優二
課程性質︰數學系大二必修
課程教師︰王振男
開課學院：理學院
開課系所︰數學系
考試日期（年月日）︰2015/04/28
考試時限（分鐘）：25
試題 :
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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