Question

For $n \in \mathbf{N}$, let $A_n=\left(-\frac{1}{n}, 2-\frac{1}{n},\right)$. Determine $\bigcup_{n \in \mathbf{N}} A_n$ and $\bigcap_{n \in \mathbf{N}} A_n$.

   For $n \in \mathbf{N}$, let $A_n=\left(-\frac{1}{n}, 2-\frac{1}{n},\right)$. Determine $\bigcup_{n \in \mathbf{N}} A_n$ and $\bigcap_{n \in \mathbf{N}} A_n$.

Mathematical Proofs: A Transition to Advanced Mathematics

Mathematical Proofs: A Transition to Advanced Mathematics

Gary Chartrand,… 3rd Edition

Chapter 1, Problem 45

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Step 1

Each interval \( A_n \) is given by \( \left(-\frac{1}{n}, 2-\frac{1}{n}\right) \), where \( n \) is a natural number. As \( n \) increases, the endpoints of the interval approach 0 and 2, respectively. Show more…

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For $n \in \mathbf{N}$, let $A_n=\left(-\frac{1}{n}, 2-\frac{1}{n},\right)$. Determine $\bigcup_{n \in \mathbf{N}} A_n$ and $\bigcap_{n \in \mathbf{N}} A_n$.

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