1、

If diverges, and a natural number, such that for any, holds, then also diverges.

如果级数发散, 且当时, 有成立, 则级数发散.

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2、

Output: the Quartet is to meet the theorem up to four natural number.

输出: 给出满足四方定理中的至多四个自然数.

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3、

In this paper, a general formula of sum of power series of natural number is given.

本文利用函数项级数,微分及排列组合等工具推导出了一个求自然数等幂和的一个一般公式.

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4、

Input: The user wilfully inputs a natural number from the keyboard.

输入: 用户从键盘任意输入一个自然数.

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5、

Output: meet guess is the natural number two.

输出: 给出满足猜想的两个自然数.

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6、

Beyond Core Knowledge: Natural Number . " Chap . 7 in The Origin of Concepts. "

核心知识之外: 自然数〉选自《概念之源 》 第七章.

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7、

Natural Number System in MS

MS中的自然数系统

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8、

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.

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。

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9、

Some properties of the Fibonacci sequence are discussed and some probability relations between the Fibonacci sequence and the natural number sequence are obtained.

讨论了Fibonacci序列的一些性质,得到Fibonacci序列与自然数序列的某些概率联系。

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10、

A recurrence formula of the coefficient of the sum of natural numbers power and the calculating formula of Bernoulli Number

自然数幂和公式系数的递推公式和有关Bernoulli数的计算公式

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11、

Probability relation between the natural number sequence and the Fibonacci sequence

Fibonacci序列与自然数序列的概率联系

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12、

This paper proves one of the two important limits with continuous function, which is different from the mathematicians' demonstration by treating x as natural number.

本文是对两个重要极限之一的证明,以往数学家们都是对x为自然数的证明,这里是以连续函数来进行证明。

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13、

Researches on Stirling number appearing in power sum of natural numbers

自然数方幂和中的Stirling数研究

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14、

In order to transform n-dimensions data into one-dimension data. The author first considers two sets: the natural number set N and the cartesian product N × N.

为了实现多维数据到一维数据的转换,本文首先考虑两个集合:自然数集N和笛卡尔积N×N。

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15、

If every fixed point of f is a interior point of T, then either every point of T is a periodic point of f with period r < n or fr has a turbulence for some natural number r < n.

如果f的不动点都在T的内部,那么,T上的每个点都是f的周期为r≤n的周期点,或存在自然数r≤n,使得,fr含有湍流。

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16、

Natural Number K Power Sum Once

关于自然数K次幂和的讨论

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17、

A study for a residual squard natural number sequence with modelo R

自然数的平方模R剩余序列的研究

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18、

In order to let high octane number natural gas to be compression ignited, measures like high compression ratio, glow plug heating, heat-isolating coating, as well as air inlet heating, are adopted in this system.

为了使高辛烷值的天然气实现压缩着火,该系统采用了高压缩比、电热塞助燃和燃烧室壁面喷涂隔热层等技术措施,并采用了进气预热。

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19、

A Generalization of Preceding N-trmed Power Sum for Natural Number

自然数前n项方幂和推广

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20、

All of these indicate that the system of Peano ′ s natural number can be generated in MS and a theoretical foundation provided to prove that MS is a foundation of classical mathematics.

这表明Peano自然数系统能在MS中产生,为最终证明精确性经典数学能奠基于MS提供了理论基础。

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