The film was a near perfect rendition of the book. The only other case I can think of like that is LOTR.
So many things about that film are spot on - the casting, the direction, the music (Pixies, Dust Brothers). Again, LOTR also hit all the right notes in that respect.
Translating a book to film is somewhat analogous to translating literature, particularly poetry, from one language to another. If the translation is too literal it risks failing in the target medium, whereas if it's too idiomatic then it risks reshaping the source material.
In the case of LOTR, as you say, the changes made for a better film, while remaining true to the source material, and so were entirely justified. The Hobbit, on the other hand, was a complete travesty, partly because they practically rewrote the story.
“Translation is that which transforms everything so that nothing changes.”
– Günter Grass
Both of these are infinite, but the set of numbers containing odd numbers is by definition smaller than the set of numbers containing all integers, because it doesn't have the even numbers.
This is provably false - the two sets are the same size. If you take the set of all integers, and then double each number and subtract one, you get the set of odd numbers. Since you haven't removed or added any elements to the initial set, the two sets have the same size.
The size of this set was named Aleph-zero by Cantor.
Euler's identity is pretty amazing:
e^iπ + 1 = 0
To quote the Wikipedia page:
The fact that an equation like that exists at the heart of maths - feels almost like it was left there deliberately.