Gödel numbering

Gödel numbering is a method devised by mathematician Kurt Gödel to encode mathematical statements and formulas as unique numbers. This system allows complex expressions to be represented in a simple numerical form. Each symbol in a mathematical language is assigned a specific number, and sequences of symbols (like statements or proofs) are then converted into a single number through a systematic process. This technique is crucial in Gödel's incompleteness theorems, which demonstrate limitations in formal systems, showing that certain truths cannot be proven within those systems. Gödel numbering thus bridges the gap between mathematics and arithmetic.