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