This is the second in a series of posts that started here. In the first post I explained what I’m up to. Now let me just continue with some more questions. I’m now on to the harder Section II questions. Here’s the first one I want to look at. Even though it makes the posts shortish, I think I’m going to stick to one long question per post.

9F. Prove the Axiom of Archimedes.

Let be a real number in and let be positive integers. Show that the limit

exists, and that its value depends on whether is rational or irrational.

[*You may assume standard properties of the cosine function provided they are clearly stated.*]

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