That's not good: We don't want to have to use words such as endowed and structure that are not precisely defined in the context and, thus, are conceptually fuz

That's not good: We don't want to have to use words such as endowed and structure that are not precisely defined in the context and, thus, are conceptually fuzzy. Some intuitive overviews, clearly labeled as such, are fine and can be helpful, but "idiomatic language" just is not. Won't find such in the writings of W. Rudin, P. Halmos, J. Neveu, or any of a long list of authors of some of the best math books. In a good math or computer science journal, a reviewer or the editor would likely reject "idiomatic language". The definitions I gave are the accepted ones.