Number Theory: There are an Infinite Number of Irrational Numbers - Part 1

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This short video details a proof of the fact that there are an infinite number of Irrational numbers. The proof only shows that this set is in fact Countably Infinite.
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Is it also true that between any 2 rational numbers (they can be infinitesimally close) that there is always an infinite number of rational numbers between them?

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