U/_3{x € Q ] 0 < x <1/i}
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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![The image displays the mathematical expression:
\[ \bigcup_{i=3}^{7} \{ x \in \mathbb{Q} \mid 0 < x < \frac{1}{i} \} \]
This expression represents the union of sets. For each integer \( i \) from 3 to 7, the set includes all rational numbers \( x \) such that \( 0 < x < \frac{1}{i} \).
**Explanation:**
- **Union (\(\bigcup\))**: The operation of combining multiple sets into one set that contains all elements from the included sets.
- **Indices (\(i=3\) to \(7\))**: The variable \( i \) ranges from 3 to 7, inclusive.
- **Set Notation (\(\{ x \in \mathbb{Q} \mid 0 < x < \frac{1}{i} \}\))**: This represents the set of all rational numbers (\(\mathbb{Q}\)) that are greater than 0 and less than \(\frac{1}{i}\).
The expression outlines the process of taking these sets for each value of \( i \) and forming a combined set with elements from each.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F047df78c-b78a-43ef-8ee4-d91e6f99fa93%2Fda8ddaf5-7ca0-4807-a43c-f0a03be1236b%2F0v2qls_processed.png&w=3840&q=75)
Transcribed Image Text:The image displays the mathematical expression:
\[ \bigcup_{i=3}^{7} \{ x \in \mathbb{Q} \mid 0 < x < \frac{1}{i} \} \]
This expression represents the union of sets. For each integer \( i \) from 3 to 7, the set includes all rational numbers \( x \) such that \( 0 < x < \frac{1}{i} \).
**Explanation:**
- **Union (\(\bigcup\))**: The operation of combining multiple sets into one set that contains all elements from the included sets.
- **Indices (\(i=3\) to \(7\))**: The variable \( i \) ranges from 3 to 7, inclusive.
- **Set Notation (\(\{ x \in \mathbb{Q} \mid 0 < x < \frac{1}{i} \}\))**: This represents the set of all rational numbers (\(\mathbb{Q}\)) that are greater than 0 and less than \(\frac{1}{i}\).
The expression outlines the process of taking these sets for each value of \( i \) and forming a combined set with elements from each.
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