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**Gödel’s incompleteness theorem**

Gödel’s first incompleteness theorem states that no axiomatic system capable of expressing arithmetics can be complete and consistent at the same time. If the axiomatic system is consistent, there will always be some arithmetical truths which will lie outside the system’s scope.

Wikipedia article on Gödel’s incompleteness theorem.

Dangerous Knowledge – BBC documentary on Cantor, Gödel and the significance of their discoveries.

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