Find U₁A, and A; if for every positive integer i, d) A, (i, co), that is, the set of real numbers x with x> i.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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**Problem 56: Set Theory**

Given the sets \( A_i \) for every positive integer \( i \), perform the following operations:

- Find the union \(\bigcup_{i=1}^{\infty} A_i\).
- Find the intersection \(\bigcap_{i=1}^{\infty} A_i\).

**Definition:**

- \( A_i = (i, \infty) \), which represents the set of all real numbers \( x \) such that \( x > i \).
Transcribed Image Text:**Problem 56: Set Theory** Given the sets \( A_i \) for every positive integer \( i \), perform the following operations: - Find the union \(\bigcup_{i=1}^{\infty} A_i\). - Find the intersection \(\bigcap_{i=1}^{\infty} A_i\). **Definition:** - \( A_i = (i, \infty) \), which represents the set of all real numbers \( x \) such that \( x > i \).
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