※ 引述《u2150260 (鴻哥)》之銘言：
: ∞ ∞
: 1. Let An=[1-1/n 2+1/n),n=1,2,3... find ∩An and ∪An
: n=1 n=1
: 2. Let a,b be real numbers and b>0. Let An be the interval (a,a+b/n]
: ∞
: for every positive integer n .Prove that ∩An is empty set.
: n=1
: 集合的問題答案要怎麼寫呢
1. ∩An=[1,2] and ∪An=[0, 3/2)
2. Suppose that a+ε is in ∩An for all n,
while a+ε is not in (a,a+b/N] as b/N <ε, such N indeed exists
by Archimedes Prop.
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