自然数

Departing from basic concepts of cardinal numbers and their numbering orders, the paper differentiated and analyzed some concepts easy to be confused related to binary system, pointing out that the introduced concepts of ordinals played an important role in the development of modern mathematics. As the foundation of SHAO Yongs mathematics, the primordial Yi, in the history of mathematics, exhibits the first specially defined ordinal system, in which the binary numbering method was used at the first time.

本文从自然数及其记数法的基本概念出发，辨析了与二进位制相关的几个容易混淆的概念，指出序数概念的引入在近代数学发展中有重要意义，作为邵雍数学学派的数学基础，先天易是数学史上第一个专门定义的序数体系，该序数体系在数学史上率先采用了二进位制记数法。

O9Z6J?Kd Abstract: Departing from basic concepts of cardinal numbers and their numbering orders, the paper differentiated and analyzed some concepts easy to be confused related to binary system, pointing out that the introduced concepts of ordinals played an important role in the development of modern mathematics.

本文从自然数及其记数法的基本概念出发，辨析了与二进位制相关的几个容易混淆的概念，指出序数概念的引入在近代数学发展中有重要意义，作为邵雍数学学派的数学基础，先天易是数学史上第一个专门定义的序数体系，该序数体系在数学史上率先采用了二进位制记数法。

The natural number set N and the cartesian product N×N.

自然数集N和笛卡尔积N×N。

For example, the cofinality of ω is ω, because the sequence ω·''m''( where ''m'' ranges over the natural numbers ) tends to ω; but, more generally, any countable limit ordinal has cofinality ω.

例如，ω的共尾性是ω，因为序列ω·''m''(这里的''m''取值于自然数之上)趋向于ω；但是，更加一般的说，任何可数极限序数都有共尾性ω。

Such a commutative law can be enlarged by induction to any two natural numbers: a+b=b+a.

这种交换性可以由归纳法原理推广到任何两个自然数的加法：a+b=b+a。

Just as λ-calcu-lus allows you to construct and reason about every possible computable function, there were high hopes that π-calculus would play similar role for concurrency.

本文提出了一个方法，据此可以把自然数和函数描述为进程，从而证明了π演算有足够的能力描述所有的可计算函数，同时还说明了与λ演算相比，π演算有着更高的计算效率。

And, like natural numbers , integers is a countable infinite set.

和自然数一样，整数也是一个可数的无限集合。

And, like natural numbers , integers are a countable infinite set.

和自然数一样，整数也是一个可数的无限集合。

This paper studies the curvilinear integral ∮ L[xn-1yn-1]/[x2n+k2y2n]where L is a sectioned smooth and no multiple points closed curve, n is some natural number, k is some positive number.

本文研究曲线积分x~(n-1y~(n-1)/x~(2n+k~2y~(2n)，其中L是公段光滑无重点的闭曲线，n为某一自然数，k为某一正数。首先利用极坐标变换将曲线积分化简，然后对n、L不同情况给出相应结果

The initial population size is studied based on the defined partial function, favor and back difference equations, and the schema theorem.

该文研究二进制和自然数编码遗传算法的群体规模，结合偏好函数和模式定理，利用前向及后向差分方程，得到这2种编码的群体规模下限值，证明其存在性。

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％。