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单词 Gödel numbering
释义
Gödel numbering

Mathematics
  • A Gödel numbering assigns to each finite word in a finite alphabet a unique natural number. As an example, if A,B,…,Z are counted as 1,2,…,26, then the word NUMBER would be assigned the number 214321513721151318. Using the primes 2,3,5,… in order and as N is the 14th letter, U the 21st, etc. As prime factorization is unique, Gödel numbering is one-to-one. See also halting problem.


Philosophy
  • A process whereby a unique number can be associated with any formula of a logical system. This is an essential step in realizing the goal of metamathematics, that the proofs of a system should themselves be treated as mathematical objects. By Gödel numbering claims made within the language about proofs and theorems may be mapped onto arithmetical claims.


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