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Let {An : n E N} be the indexed collection of sets defined by 1 2, 2+ 2n An Prove that: nMeN An = Ø

Let {An : n E N} be the indexed collection of sets defined by 1 2, 2+ 2n An Prove that: nMeN An = Ø

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let \(\{ A_n : n \in \mathbb{N} \}\) be the indexed collection of sets defined by \[ A_n = \left(2, 2 + \frac{1}{2^n}\right) \] Prove that: \[ \bigcap_{n \in \mathbb{N}} A_n = \emptyset \]
Transcribed Image Text:Let \(\{ A_n : n \in \mathbb{N} \}\) be the indexed collection of sets defined by \[ A_n = \left(2, 2 + \frac{1}{2^n}\right) \] Prove that: \[ \bigcap_{n \in \mathbb{N}} A_n = \emptyset \]
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