For a course, I am required to do a presentation. The topic could either be something mundane, like a career strategy report, or something more interesting, such as a controversial topic, or an exposition on something you find interesting. What I would like to do is to present math in a way that probably no one in the class, other than myself, has seen before. That is to say, math as a deeply conceptual subject that does not necessarily involve computation with literal numbers.
In order to illustrate what I mean by the above, I would present the following theorem: There are at least two kinds of infinite sets: Countable ones, and uncountable ones (of course I would define bijection and countable). I would present the diagonal argument, since it is elegant, ingenius, noncomputational, and short.
My question is whether or not the general public (nonmathematicians) would be able to understand the argument. Note, I would not be explicit about the axiom of choice, etc.