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Problem 62: (The Union And Intersection Of Infinitely Many Open Sets)

For each $n\in\mathbb{N}$, let $A_n = \left(0,1+\frac{1}{n}\right)$.

  1. What are the sets $\ds \bigcup_{n=1}^\infty A_n$ and $\ds \bigcap_{n=1}^\infty A_n$?
  2. Prove your claims.

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