论文标题
Collatz轨迹的密度
Density of Collatz Trajectories
论文作者
论文摘要
在本文中，我提出了一种研究的新方法，用于研究由集合$ s \ subset \ mathbb {n} $生成的collatz轨迹的密度。此方法用于提供$ d（\ {y \ in \ mathbb {n}：\的替代证明：最后，我简要讨论本文中提出的想法如何用于改善$ d（\ {y \ in \ mathbb {n}中的结果：\ cestists k \ text {where} t^k（y）<y）<y^c \}）= 1 $ for $ c> \ log_4 3 $。
In this paper I present a new method of studying the densities of the Collatz trajectories generated by a set $S \subset \mathbb{N}$. This method is used to furnish an alternative proof that $d(\{y \in \mathbb{N} : \exists k \text{ where } T^k(y) < cy\}) = 1$ for all $c > 0$. Finally, I briefly discuss how the ideas presented in this paper could be used to improve the result that $d(\{y \in \mathbb{N} : \exists k \text{ where } T^k(y) < y^c\}) = 1$ for $c > \log_4 3$.
