自然数

In the second part, we consider the intrinsic structure of the partition of ω, study the separativity of the orders (ω,≤ and discuss the distributivity of the lattices

本文第二部分通过研究自然数分拆的内在结构，讨论偏序(ω，≤的可分裂性，以及格(ω，≤的可分配性，我们证明了存在一个偏序它是可分裂的，但由它诱导的格却是不可分配的。

What is the smallest number that is evenly divisible by all of the numbers from 1 to 20?

问最小的一个可以被1到20之间所有数整除的自然数是多少？

It is greatly efficient, because this overcomes the shortcoming of Eratosthenes algorism that need compare every natural number in the given range, This algorism can acquire all prime numbers between 1 and any given natural number m This article also has given the complexity of the algorism, and even if sift in the algorism were different, it will be...

这避免了传统Eratosthenes 筛法需要比较每个数的缺点，极大地提高了算法效率。该算法能用于求1至任意自然数m之间的所有素数。同时还给出了该算法的最多比较次数公式，即使用不同的筛子利用该公式也容易求得其最大比较次数。

These sets are interesting subsets of natural number in combinatorial number theory, ergodic theory and topological group.

这些集合是人们在组合数论、遍历理论以及拓扑群中感兴趣的重要的自然数子集。

If you can take any natural number N, then the corresponding series is called geometric series .

如果N可以取任意自然数的话，相应的数列叫作几何级数。

Mathematical induction is an important method in mathematics.

数学归纳法是数学中一种重要的证明方法，也是中学数学一个非常重要的内容，用于证明与无穷的自然数集相关的命题。

It is pointed out that the complete infinite sequence of natural numbers cannot consist of only finite ordinals, thus a kind of so-called "potential tail" may be defined.

指出了一个完全的自然数无穷序列不可能由且仅由无穷多个有穷序数去组成，如此就引进并定义了叫做"潜尾"的概念。

We can draw a conclusion from the comparison between natural number and meaning that both exactness and fuzziness are meaningful only lying in a cognitive field and the former is relative, which can only exist at a static and close system; while the latter is universal, which is the result of being the cognitive reference point. Both exactness and fuzziness come from the interaction of the cognitive subject and object, and they are dialectical and unitive, based on the historicity and infinity of human cognition, which determines what we can do, is just to hold the continuum by discreteness and infiniteness by definiteness.

从自然数与意义对比得出的结论是：精确性只存在于一个静态的封闭系统中，是相对的，模糊性是语言充当人类认知参照点的结果，是绝对的，这两个概念都只有放在某个人类认知场才有意义；精确性和模糊性都来源于认知主体和客体的相互作用，它们是辩证统一的，其辩证统一的基础在于人类认识的历史性、无限性决定了人类只能够用离散来把握连续、用有限去追求无限。

The cover pebbling number for lexicographic product graphs and some strong product graphs were determined.

对一个图而言，满足此条件的最小的自然数即为此图的覆盖数。

On the basis of introducing the fixed point of Banach theorem, this paper firstly elaborates the important application of the existence of the solution of the linear algebraic equation and the ordinary differential equation, then it narrates the important application of obtaining the leading Newton repetitive process and the natural number the inferior square root and the equation root in the approximate calculation.

本文在介绍Banach不动点定理的基础上，首先阐述了其在线形代数方程、常微分方程解的存在性中的重要应用；然后讲述了其在求导Newton迭代法、求自然数的次平方根、求方程根的近似计算中的重要应用；最后，介绍了其在求一类递推数列极限中的应用。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。