In mathematical logic, a Gödel numbering is a function that assigns to each symbol and well-formed formula of some formal language a unique natural number, called its Gödel number. The concept was first used by Kurt Gödel for the proof of his incompleteness theorem.
A Gödel numbering can be interpreted as an encoding in which a number is assigned to each symbol of a mathematical notation, after which a sequence of natural numbers can then represe...
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In mathematical logic, a Gödel numbering is a function that assigns to each symbol and well-formed formula of some formal language a unique natural number, called its Gödel number. The concept was first used by Kurt Gödel for the proof of his incompleteness theorem.
A Gödel numbering can be interpreted as an encoding in which a number is assigned to each symbol of a mathematical notation, after which a sequence of natural numbers can then represent a sequence of strings. These sequences of natural numbers can again be represented by single natural numbers, facilitating their manipulation in formal theories of arithmetic.
In the time since Gödel's paper was published in 1931, the term Gödel numbering has come to be used for a variety of more general assignments of mathematical objects to natural numbers.
Gödel used a system of Gödel numbering based on prime factorization. He first assigned a unique natural number to each basic symbol in the formal language of arithmetic he was dealing...
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