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Discrete Mathematics & Math
Q82 / 100
What is the Gödel incompleteness theorem?
Correct! Well done.
Incorrect.
The correct answer is B) Any consistent formal system capable of basic arithmetic contains true statements that cannot be proved within the system; it also cannot prove its own consistency
B
Correct Answer
Any consistent formal system capable of basic arithmetic contains true statements that cannot be proved within the system; it also cannot prove its own consistency
Explanation
First Incompleteness: any consistent, complete, recursively enumerable formal system (containing PA) is incomplete — there are true but unprovable statements. Second: such a system cannot prove its own consistency. Profound limits on formal mathematics.
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