考拉兹猜想數值連續膨脹現象之規律探討分析與歸納 Exploratory and Inductive Analysis of the Patterns of Consecutive Expansion in the Collatz Conjecture

此探討內容已進行重大更新,將會在確認新的六大模型都正確後盡快將新版內容上傳於此。 本報告整理並分析了考拉茲猜想中數值連續膨脹的現象,初步提出具規律性且可預判的現象與推論模型,並嘗試將模型拓展至無限大。然而拓展過程中會出現無限大作為指數的表達式,因此模型的推論與完整性仍有待進一步討論。 本報告為大學生(即作者本人)於寒假期間的自主學習成果。由於研究過程中得到的初步結論可能有助於理解猜想的推論與結構性分析,故上傳至此供參考。 勘誤:在第11頁拓展與驗證終「而根據上述理論可以知道此奇數可做𝑛 − 1次膨脹,無法做到 n次膨脹」有誤,應該為「而根據上述理論可以知道此奇數可做x − 1次膨脹,無法做到 x次膨脹」。 作者對英語不精通,檔案內英文翻譯皆由 ChatGPT 與 Google 翻譯協助完成,如有語句不通或語意不精確,還請見諒;中文表述較為精準。 This report presents an analysis and synthesis of the consecutive expansion phenomenon in the Collatz conjecture. Preliminary patterns and heuristic models are proposed, and an attempt is made to extend the models to infinity. However, this extension leads to expressions involving infinity as an exponent, so the proposed models require further discussion and validation. This report represents the independent study of an undergraduate student during the winter break. Since the preliminary results may contribute to understanding the conjecture’s reasoning and structural behavior, it is uploaded here for reference. The author is not proficient in English. The English translation of this document was assisted by ChatGPT and Google Translate. Any awkward phrasing or imprecise expressions are regretted; the original Chinese version conveys the meaning more accurately.