Off My Chest
RULES:
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X = "Nobody checks out books anymore": less extreme. People could go to be going to the library and choosing to read books there.
Y = "let alone visits the library": more extreme. People don't even go to the library, so they wouldn't be able to check out books even if they wanted to.
Why is that usage not correct? According to you definition, it should be. We it the other way around, then it would be wrong (according to your definition).
Please explain.
You are getting confused because you are comparing negations. It's "visiting the library" that is less extreme than "checking out a book".
This is also more of an example of dependency rather than extremity. That is, "checking out a book" could only happen if "visiting the library" happened first. So you could say "I never even travelled to North Korea, let alone bought a souvenir there" -- while buying a souvenir is small compared to travelling to NK, the travelling would have to happen first, so the phrase makes sense.
This is not confusion, but a different view point, just like 6 is 9.
In the previous example with the library, at least people are still reading books in a library. One should be happy that the library is being used. However, if people don't even go to a library, that is more extreme because its existence will be futile.
"I've never bought a souvenir in North Korea, let alone traveled there." is just another way to phrase the same fact from a different view point. Buying souvenirs is trivial and it would be trivial, if I had ever been to North Korea, and since I haven't, it's the more extreme of the two.
Do you understand now?
You can't check out a book if you don't go to the library. What I mean by more extreme is this, that it requires the first one as a prior condition, or is otherwise asserted to be less likely to happen.
My on the spot made up definition may not have been the clearest :)
First I'd like to clarify how I interpreted OP's phrase: I think they meant "check out book" to specifically mean "borrow from the library". Seems like you came to the same interpretation, but I just wanted to mention that for anyone else who might be confused reading this, because "check out" has broader usage that could just mean "look at" without any implied reference to a library,
In that context, "visiting the library" is a prerequisite of checking out a book, so it's less extreme. You cannot possibly check out a book without first visiting the library, but you can (as you point out) visit the library without checking out books.
"Nobody visits the library" would imply that nobody checks out books, while "nobody checks out books" does not imply that nobody visits the library.
The part after "let alone" should already logically follow from the part before. If you were to break down the task into steps, it should follow the pattern of "nobody finishes step 1, let alone step 2".
Step 1: Visit a library
Step 2: Check out a book from the library
Does that make sense?