Math Problem Statement
Sei I ein Intervall in R, das mehr als einen Punkt enthält, und seien f : I → R und 9: I → R stetige Funktionen. Für alle x E In Q sei f(x) = g(x). Beweisen Sie, dass f(x) = g(x) für alle x € I gilt.
Solution
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Math Problem Analysis
Mathematical Concepts
Continuity
Density of Rational Numbers
Real Analysis
Formulas
f(x) = lim_{n → ∞} f(x_n) for x_n → x
g(x) = lim_{n → ∞} g(x_n) for x_n → x
Theorems
The density of rational numbers in real numbers
The continuity property of limits
Suitable Grade Level
Undergraduate (Real Analysis)
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