对五个问题的回答

自公元前六世纪毕达哥拉斯在数学中提出单子概念开始,数学中就出现了不可分量的概念。此文在对第一个问题的回答中对不可分量下了严格的定义。在对第二个问题的回答中指出:将有理数与有理数组成的空集合结合在一起排序,这是实数理论的基础,是引进无理数的基本办法。作者只是发展了这一办法,定义了个由三元组表示的偏心的区间套组成的Dedekind分割并确定了不等式0<<,m∈N。这样是一个标准的无穷小,数学上的不可分割的量和毕达哥拉斯所期望的单子。在对第三个问题的回答中指明我们现在不用Lebesque测度,只讨论区间和区间套的测度。并指出:我们已在先行的文章中证明了“实数集R的测度为零”,而在Lebesque测度中认定“实数集R的测度大于零”。这是Lebesque测度中的头号悖论。在对第四个问题的回答中指出无理数e和π满足不等式:0

A Reply to Five Problems

Since Pythagorean put forward the concept of monad, then indivisibles have appeared in mathematics lasted for twenty-five hundred years or more. In the paper in the reply to the first problem, the author gives a rigorous definition to indivisibles. In the reply to the second problem, the author points out the fact that ordering the rational numbers and the empty sets produced by the interval nests of rational numbers, is the foundation of real number theory and the basic method to introduce irrational numbers. The author is only to develop the method, and defines a triad representation off-centered interval nestsorganized Dedekind cut and inequalities Then to is a standard infinitesimal,mathematically indivisible, and an monad expected by Pythagorean. In the reply to the third problem, the author points out the fact that we do not use Lebesque measure now. We discuss only the measure of interval or interval nests of real numbers. We have proved that the measure of real number set is equal to zero. However the Lebesque measure theory claims that the measure of real number set is greater than zero. This is the first paradox in Lebesque measure theory. In the reply to the fourth porblem the author points out the fact that the irrational numbers e and π satisfy the inequalities; 0