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Recently, in an Analysis class, I was tasked with proving that the dyadic rationals are dense in R (which can be proven by the archimedean property).
The dyadic rationals are defined as:
$$\left\{ \dfrac{m}{2^n} \; | \; m \in \mathbb{Z},\; n \in \mathbb{N} \right\}$$
Your Goal: for two real numbe...