Every rational number x may be written in the form x = m/n with n > 0 and m, n coprime integers. Define the function f : (0, 1) → R with { 0 f(x) = { At which points is f continuous? n if x irrational if x rational and x = m n
Every rational number x may be written in the form x = m/n with n > 0 and m, n coprime integers. Define the function f : (0, 1) → R with { 0 f(x) = { At which points is f continuous? n if x irrational if x rational and x = m n
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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![Every rational number \( x \) may be written in the form \( x = m/n \) with \( n > 0 \) and \( m, n \) coprime integers. Define the function \( f : (0, 1) \to \mathbb{R} \) with
\[
f(x) =
\begin{cases}
0 & \text{if } x \text{ irrational} \\
\frac{1}{n} & \text{if } x \text{ rational and } x = \frac{m}{n}
\end{cases}
\]
At which points is \( f \) continuous?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe15ed467-90ec-4e60-afef-3d3f6119f74d%2Fe177c6e7-b519-46ea-860d-3f379c2d25a7%2F8gu7djk_processed.png&w=3840&q=75)
Transcribed Image Text:Every rational number \( x \) may be written in the form \( x = m/n \) with \( n > 0 \) and \( m, n \) coprime integers. Define the function \( f : (0, 1) \to \mathbb{R} \) with
\[
f(x) =
\begin{cases}
0 & \text{if } x \text{ irrational} \\
\frac{1}{n} & \text{if } x \text{ rational and } x = \frac{m}{n}
\end{cases}
\]
At which points is \( f \) continuous?
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