关于双射函数f:N×N×N→N的研究

Study on Bijective Function f:N×N×N→N

讨论了可数无穷个可数无穷集合的并的计算问题。通过对自然数集合N的二次笛卡尔积运算———N×N和三次笛卡尔积运算———N×N×N的详细分析,得出了它们与自然数集合N之间都存在双射关系结论,即集合N×N和集合N×N×N都是可数无穷的。文中推导出了自然数集合N的三次笛卡尔积运算———N×N×N与自然数集合N之间的双射函数运算公式,对可数无穷集合的复杂计算作了进一步研究。得出结论:任意可数无穷个可数无穷集合的并(如N×N×N×…,即Nn)也是可数无穷的。

Discusses the computational problem about union of countable infinite of countably infinite sets. Through the analysis of the second power Cartesian product of natural number set N——N×N and the thirdpower Cartesian product of natural number set N——N×N×N,obtains the conclusion that they all have the bijective relation to natural number set N,it means that the set N×N and the set N×N×N are all countably infinite.Deduces the operational formula of the function between the third power Cartesian product of the natural number set N——N×N×N and N,and further researches into complex computation of countably infinite sets. In the end it points out that the union of countable infinite of countably infinite sets ( such as N×N×N×…, that is Nn) is also a countably infinite set.