^§This proof, known as Gödel’s Incompleteness Theorem, as well as associated proofs from computation and complexity theories, are far more elegant than I can express here. Interested readers are referred to Douglas R. Hofstadter’s massive work Gödel, Escher, Bach: An Eternal Golden Braid or to the smaller and less readable but much more complete Computability and Complexity Theory by Homer and Selman.