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I already did it.
Ok, for anyone intrigued but not interested in nerdy maths stuff:
A vacuous truth is a statement about an empty set of objects. Eg. all six-legged giraffes are green. The assertion that some giraffes are green would be false, but the statement as a whole is true because it's limited to an empty subset of giraffes. You can't find a six-legged giraffe that's not green.
As soon as you're in a room with no books, your job is done.
Btw "in this room all the books that each book references may also be found in this room" != "if the book isn’t in this room no other book references it".
In mathematical terms you have a directed acyclic graph where books are nodes and citations are edges. You're expanding your collection by following directed edges.
At some point you'll run out of outward edges to follow, that's the "in this room all the books that each book references may also be found in this room". But you can still have inward edges, ie. other books that cite your books but you don't know about them because your books don't cite them.
And you _will_ most likely run into this situation because the graph is acyclic, ie. by picking any node (book) and following edges you'll never visit a node you've already visited.
In simpler terms, you can only discover older books this way, but newer books can cite them. "If the book isn’t in this room no other book references it" isn't future-proof too
@gronostaj I see what your saying and i think you are miss interpreting what I stated.
I no way did I mean that I am collecting all the books that exist that reference the books I have. That would be impossible todo since new books continue to be written
What I am doing is taking the books I have... making a list of the books or articles etc that are referenced in the books I have....
As the books I buy moving forward come in I will log the references they contain, and add the books that are not in the collection to the current list of books to get “next”..
I think there could be a point where i have a closed loop. As a book cannot reference a book that does not exist.
The problem you state would be for the situation where I continue to buy books that contain references to the books I have... and the continue to find references in books I don’t have for the books I do have...
I’m looking for references in the books I have for books I don’t have..
Two very different situations. One way could create a self contained system the other could lead to a never ending task as long as more books continue to be published.
Ahh, I've completely misinterpreted the “if the book isn’t in this room no other book references it” part. Sorry, my bad!
@gronostaj yeah the no other book references it, was referring to no other book in this ROOM references it.
But I can see the grammatical confusion.
I guess how would one properly describe the situation saying if a book isn’t in this room then no book in this room references it, also the only way a book can come into this room is if it was referenced by a book already in the room.