Can you prove the Archimedean property of the rational numbers without constructing the reals and using the least upper bound property? It seems odd to have to take this roundabout approach, but I don't know any proof that avoids it.
Archimedean property of the rational numbers
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analysis
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0I came across this question at p.19 in "Principles of Mathematical Analysis Third Edition" by Walter Rudin. – 2018-12-02