Thework of Kurt Gödel has shown that no useful system of arithmetic can beboth consistent and complete: see Gödel's incompleteness theorems.

工作哥德尔表明，任何有用的系统算法可以是一致的和完整的：见哥德尔的不完备性定理。

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The main conclusion of Gödel’s incompleteness theorems is that all logical systems will have statements that cannot be proven or disproven; therefore, all logical systems must be “incomplete.”

高德的不完备定理的主要结论是，所有的逻辑体系都会存在无法证明或证伪的命题。 因此，所有的逻辑体系都不“完备”。

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