User blog comment:Simplicityaboveall/Simplicity/@comment-2033667-20141225175235/@comment-1605058-20141226085031

I have to disagree. If I were a layman, I'd be very glad if someone has described to me notion of set in better detail, for few reasons. First, notion of "set" is quite abstract, and, as Vel mentioned, it's very worth pointing out that set doesn't contain repetitions and order in them doesn't matter. Second, if you are talking about sets as "series" of elements, it's not immediately clear why some infinite sets are such "series". For example, when we talk about set of all ordered pairs of integers it's not immediately clear to a layman how to make it into a series. "I think (0,0) would be first, but should (1,0) or (0,1) be next? Or maybe (-1,0)?" - this is what average layman could think. Even worse, there are sets which you can't write as a reasonable series. You should be perfectly aware of the fact that you cannot write all real numbers one by one, which is layman's expectation of what series should look like. Third, you have to let your readers know that sets aren't just rigid objects, but that you can perform operations in them, such as union or intersection. Such mental activities are really helpful when trying to understand the very notion of a set.