# Gödel's incompleteness theorem

- the theorem that states that in a formal logical system incorporating the properties of the natural numbers, there exists at least one formula that can be neither proved nor disproved within the system.
- the corollary that the consistency of such a system cannot be proved within the system.

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## Origin of Gödel's incompleteness theorem^{}

after K. Gödel, who formulated it

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Based on the Random House Unabridged Dictionary, © Random House, Inc. 2018