 Assume furthermore that F is consistent, i.e., it will never derive false statements form true ones. In his proof Gödel used the coding possibilities of multiplication to construct an image of the system (see the discussion of   Gödel numbering  from the entry on Gödel’s Incompleteness Theorems).  According to the fundamental theorem of arithmetic   any number can be uniquely factored in to its primes. This defines a one-to-one relationship between multisets of numbers and numbers: the number 12 can be constructed on the basis of the multiset \(\{2,2,3\}\) as \(12=2 \times 2\times 3\) and vice versa. This allows us to code any sequence of symbols as a specific individual number in the following way: