A Continuous Function is DETERMINED by its values at Rational Numbers! | Calculus Proof!

We prove that a continuous function from the real numbers to itself is COMPLETELY determined by its values at ONLY the rational numbers. The video is a beautiful introduction to rigorous proof-based math in the context of calculus and continuous functions. In the proof, we rigorously explain why the rational numbers are "dense" in the real numbers, by considering the decimal expansion construction of the real numbers. The video is designed for calculus students, real analysis students, and anyone interested in rigorous mathematics, and fun short mathematical proofs.

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