When are activerecord associations made?

Hello,

My question is when ActiveRecord associations are actually made? To
me, it doesn't seem like the relationship is made until of the objects
is saved into the database. Let's say i have models like:

Library has_many :books
Book belongs_to :Library

If I have code such as:

book = Book.new

library = Library.new
library.books << book

it seems like library.books is empty UNTIL book is first saved.

this causes strange problems for me if I am trying to validate that a
book always belongs to a library, and a library has to have a least
one book.

Maybe I'm thinking about this the wrong way?

Thanks in advance,
Chris