2. Consider f: R→ R with f(x) = x rational x irrational Show that f is discontinuous at every real number.
2. Consider f: R→ R with f(x) = x rational x irrational Show that f is discontinuous at every real number.
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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![**Problem Statement:**
2. Consider \( f: \mathbb{R} \to \mathbb{R} \) with
\[
f(x) =
\begin{cases}
1 & \text{x rational} \\
0 & \text{x irrational}
\end{cases}
\]
Show that \( f \) is discontinuous at every real number.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd597ffd2-5c4b-4c2e-8332-77ce1607dac1%2Fdc1435bf-5259-4f94-896a-a5067c04a203%2F6kv5l1c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
2. Consider \( f: \mathbb{R} \to \mathbb{R} \) with
\[
f(x) =
\begin{cases}
1 & \text{x rational} \\
0 & \text{x irrational}
\end{cases}
\]
Show that \( f \) is discontinuous at every real number.
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