※ 引述《smartlwj (實變我好愛你)》之銘言：
: Prove that
: If An= {m/n : m ε Z}
: then limsup An = Q and liminf An = Z
: n→∞ n→∞
: 請問這該怎麼做呢??
: ∞ ∞
: 本來是想說用 limsup An = ∩ ∪ An
: n→∞ j=1 n=j
An<=A(n*k), for k=1,2,3,...
∞
: ∪ Ak = Bj
: k=j
hence, m/n in A(n), A(2n), A(3n),....
m/n in Bj for every j>=n
but B1>=B2>=B3.....
m/n in Bj for j=1,2,3....
m/n in ∩Bj=limsup An
if z in ∩Bj then z in B1=Q
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