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.