I just finished reading W.V.O. Quine's textbook, Mathematical Logic. It only took me about 3 years to finish it (literally), and it was by far the most difficult book I have ever read, but it was worth it. The book defines predicate logic, basic set operations, natural, rational, and real numbers, arithmetic, and some other things all in terms of set membership, universal quantification, and joint denial. Then it proves and explains a version of Godel's Incompleteness Theorem. It is fascinating stuff. I hope I'll understand it all someday.
To celebrate, I wrote in truly nerdy fashion a Perl script to generate the natural number one expressed in terms of class membership, class abstraction, universal quantification, and joint denial, according to Quine's definitions. Here it is.