哥德爾不完備定理 (Godel's Incomplete Theorem)

導論篇

計算理論簡介

計算理論的歷史

可計算性

可計算性簡介

圖靈機

不可計算問題

遞歸可枚舉

不完備定理

複雜度

複雜度簡介

複雜度理論

NP-Complete

隨機複雜度

密碼學理論

趨近演算法

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簡體版

English

Incomplete Theorem (Godel)

Sound : every theorem is a logically valid well form formula.
Consistent : no well form formula V such that { |- V } and { |- not V }.
Complete : every logically valid well form formula is a theorem.
Incomplete Theorem : 
    Natural Number System is consistent but incomplete, that is, 
    there is a closed well form formula V such that neither { |- V } nor { |- not V }

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