Other problems that only arise on families of objects can be similarly difficult to grok for beginners. E.g.: any given finite-dimensional vector space is isomorphic to its dual and to its double dual in many ways, but for the latter you can choose a (“natural”) isomorphism consistently over all such spaces, while for the former you can’t. “Why isn’t it naturally isomorphic? The bases are of the same length! What do we care if it depends on the basis or no? Why do we not care all those other proofs choose bases then?”