基于对偶恒等式对哥德尔不完备性定理、P-NP问题、芝诺悖论和连续统假设的符号理解
A dual identity based symbolic understanding of the Godel's incompleteness theorems, P-NP problem, Zeno's paradox and Continuum Hypothesis
摘要：
本文对形式系统进行了语义分析，指出了形式系统基于“行为状态”和“存在状态”的符号定义的二重性。我们证明，当这些国家被定义在一种相互对立的方式，它会导致矛盾。这导致了形式系统的不完备性，正如哥德尔定理所描述的那样。然后，我们着手解决P-NP问题，我们证明这是哥德尔定理本身的表现。然后，我们讨论芝诺悖论，并将其与上述对偶性联系起来，但与离散空间和连续空间有关。证明了连续空间中无理数表示的一个重要定理。我们扩展的结果触及的连续统假设，并提出了一个新的符号空间概念，它可以解决离散和连续的要求。我们把这种新的数学框架称为“混合空间”。
英文摘要：
A semantic analysis of formal systems is undertaken, wherein the duality of their symbolic definition based on the "State of Doing" and "State of Being" is brought out. We demonstrate that when these states are defined in a way that opposes each other, it leads to contradictions. This results in the incompleteness of formal systems as captured in the Godel's theorems. We then proceed to resolve the P-NP problem, which we show to be a manifestation of Godel's theorem itself. We then discuss the Zeno's paradox and relate it to the same aforementioned duality, but as pertaining to discrete and continuous spaces. We prove an important theorem regarding representations of irrational numbers in continuous space. We extend the result to touch upon the Continuum Hypothesis and present a new symbolic conceptualization of space, which can address both discrete and continuous requirements. We term this new mathematical framework as "hybrid space".
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
