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I'm a senior pure math student, and we have to do a final project for my real analysis class this semester. Right now I have two topics that interest me, but they seem too broad. The two topics are "non-standard analysis" and "ordinals and cardinals." The former is by far my favourite, but I don't know how to approach it. I.e. I need an interesting question in regards to it, or a fun theorem or unexpected result in non-standard analysis that my project can be centered on; I don't want to just start defining what infinitesimals are, without having a clear objective.

Does anyone have any suggestions? I'd greatly appreciate it.

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    Hah, it's funny that you mention Banach-Tarski. Unfortunately, someone already grabbed that topic before I even had a chance to do some research on it :(. Good suggestion, though, thanks. That's the kind of thing I'm looking for (but maybe related to non-standard analysis or ordinals/cardinals).2012-01-08

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