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I have tried to solve the following question but I haven't gotten an answer. Show that:

  1. $\lim\ [0,1-1/n] = [0,1)$.

  2. $\lim\ [0,1-1/n) = [0,1)$.

all the limits having $n\to\infty$.

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    Should the second problem be the same as the first?2011-11-04
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    @AD. In 1. you have open intervals while in 2. you have closed intervals on the left hand side.2011-11-04
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    Both sequences of sets $(A_n)$ are increasing hence their limits are the unions of the $A_n$. Every $A_n$ is included in $A=[0,1)$ hence the two limit-sets are subsets of $A$. It remains to show that, in both cases, every $x$ in $A$ belongs to some $A_n$.2011-11-04
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    @t.b. Ahh... I see thanks =)2011-11-04

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