Gödel’s Incompleteness theorems are two theorems of mathematical logic that demonstrate the inherent limitations of every formal axiomatic system capable of modelling basic arithmetic.
The first incompleteness theorem: No consistent formal system capable of modelling basic arithmetic can be used to prove all truths about arithmetic.
In other words, no matter how complex a system of mathematics is, there will always be some statements about numbers that cannot be proved or disproved within the system.
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