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Gödel Number

A Gödel number is a unique number associated to a statement about arithmetic. It is formed as the Product of successive Primes raised to the Power of the number corresponding to the individual symbols that comprise the sentence. For example, the statement $(\exists x)(x=sy)$ that reads ``there Exists an $x$ such that $x$ is the immediate successor of $y$'' is coded


where the numbers in the set (8, 4, 13, 9, 8, 13, 5, 7, 16, 9) correspond to the symbols that make up $(\exists x)(x=sy)$.

See also Gödel's Incompleteness Theorem


Hofstadter, D. R. Gödel, Escher, Bach: An Eternal Golden Braid. New York: Vintage Books, p. 18, 1989.

© 1996-9 Eric W. Weisstein