+* At several places they talk about some things being *real extensions* of other things. This confused me at first, because they don't ever define a notion of "real extension." (They do define what they mean by "extensions.") Eventually, it emerges that what they mean is what I'd call a *proper extension*: an extension which isn't identical to the original.
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+* Is that enough? If not, here are some [more hints](/hints/assignment_7_hint_2). But try to get as far as you can on your own.