Letf, g be continuous from R to R, and suppose that f(r) = g(r) for all rational numbers r. Is it true that f(x) = g(x) for all x ER?
Letf, g be continuous from R to R, and suppose that f(r) = g(r) for all rational numbers r. Is it true that f(x) = g(x) for all x ER?
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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Transcribed Image Text:Let \( f, g \) be continuous from \( \mathbb{R} \) to \( \mathbb{R} \), and suppose that \( f(r) = g(r) \) for all rational numbers \( r \). Is it true that \( f(x) = g(x) \) for all \( x \in \mathbb{R} \)?
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