 Besides using Gödel numbering to encode unique sequences of symbols into unique natural numbers (i.e.place numbers into mutually exclusive or one-to-one correspondence with the sequences), we can use it to encode whole “architectures” of sophisticated “machines”.For example, we can encode Markov algorithms, or Turing machines into natural numbers and thereby prove that the expressive power of recursive function theory is no less than that of the former machine-like formalizations of algorithms.