gödel's incompleteness theorems

Gödel's incompleteness theorems are two mathematical results that show the inherent limitations of formal systems, like those used in mathematics. These theorems, proved by Kurt Gödel in the 1930s, demonstrate that there will always be statements within a formal system that cannot be proven true or false within that system itself. This implies that no consistent and complete system can prove all truths about arithmetic, and there will always exist undecidable propositions.

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