Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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use Mathematic Induction

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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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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