 Roughly, one proceeds as follows: First, the primitive symbols of the language are paired with distinct natural numbers, “symbol numbers”. A little number theory then suffices to code sequences of numbers by single numbers. Consequently, well-formed formulas, as sequences of primitive symbols, are each assigned a unique number. Finally derivations, or proofs, of the system, being sequences of formulas, are arithmetized, and are also assigned specific numbers. Such a code, the “Gödel number” of a formula \(A\), is denoted as \(\ulcorner A\urcorner\), and similarly for derivations.