Collatz猜想中通常迭代下数集与奇偶矢量集间的一一映射

One-one Mapping Between the Set of Natural Numbers and the Set of Parity Vectors under Ordinary Iteration in the Collatz Conjecture

讨论了自然数与奇偶矢量间的关系 ,证明了数集Mk ={ 1,2 ,3,… ,2 k}与长为k的子奇偶矢量vk ={x0 ,x1,x2 ,… ,xk-1}的集合间存在一一映射 ,并由此得到 :设V表示所有奇偶矢量v ={x0 ,x1,x2 ,… }的集合 ,则映射σ :N→V

The relation between the natural numbers and the parity vectors is discussed. It is shown that let M k={1,2,3,...,2 k},and V k denote the set of all v k of truncations up to the kth term,viz.,{x 0,x 1,x 2,...,x k-1 }of the parity vecter v={x 0,x 1,x 2,...},if n∈M k,and n→v k(n),then the mapping σ k:M k→V k is one to one.The following result is obtained:Let V denote the set of all parity vector v={x 0,x 1,x 2,...},if n→v(n),then the mapping σ: N→V is one_to_one.