自然数

Question for thinking: C hoose 3 natural numbers from 1 to 100. If the sum of them is a multiple of 3, how many kinds of selections can you get?

思考题：从1至100这100个自然数中取3个数，若这3个数的和恰为3的倍数，有多少种不同的取法？

Indeed, the first mathematical structure-the set of natural numbers- is a semiring.

我们遇到的第一个数学结构——自然数集，就是一个半环。

As their application, we obtain some indentities for the infinite products from the new expression in the special cases of these fuctions, and establish simultaneously a kind of inequalities with their convexities.

作为应用，在特殊情况下得出了这些广义函数的新的表达式，由此出发得到了一些关于自然数和合数的无穷乘积的恒等式，同时由广义函数各种凸性建立了若干解析不等式。

The cover pebbling number of a graph,γ, is the minimum number of pebbles such that through a sequence of pebbling moves, a pebble can eventually be placed on every vertex simultaneously, no matter how the pebbles are initially distributed.

显然存在某个自然数，当图的所有点上的小石块的总数大于或等于它时，无论小石块在图上是如何初始分布的，都可以经过一系列的上述步骤，使得每个点上都至少有一个小石块。

Triviality of a natural number N is the ratio of the sum of all its proper divisors to the number itself.

一个自然数N的&Triviality&被定义它所有的Proper约数之和与它本身的比值。

The prime number is a natural number that has exactly two different divisors, i.e.

质数是指仅有两个约数的自然数，例如，1不是一个质数。

Including 0 is now the common convention among set theorists, logicians, and computer scientists.

零是一个非常奇特的数。自然数集合为N，也叫正整数。楼上说改了，那么是什么情况？

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。

That is a magic square to n * n natural numbers line up every trip, every out, and each diagonal figures and hav...

幻方即1至n*n自然数排成的每行、每列、每条对角线数字之和均相等的方阵。这是一个流行的解法。

There are natural numbers, negative numbers, rational numbers, irrational numbers, and many others

有自然数，负数，有理数，无理数和很多其他的数值。

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％。