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

I agree with Peng's point about going into more detail. In general, I would advise that you go into much more detail about all the topics that you're discussing if you intend to make them accessible to laymen. For example, you talk about sets for maybe two paragraphs. A nonmathematician might need a whole chapter's worth of explanation to be able to really internalize the concept of a set! For example, you may need to explain that sets ignore duplicate elements, and that they don't have any order, and that they can nest within each other, that they can contain (almost) any mathematical object, etc. It would also be a good idea to introduce the membership relations, subsets, unions, intersections, etc. These are non-obvious things that the reader is left to infer.

(While I'm at it, your definition of a set -- a "series of elements" -- is incorrect. The term "series" implies that there's some sort of order to sets, which there isn't.)