factorial

简明释义

英[fækˈtɔːriəl]美[fækˈtɔːriəl]

adj. 因子的，阶乘的

n. [数] 阶乘

英英释义

单词用法

同义词

反义词

例句

1.Then, because num is greater than 0, factorial will be called again, this time with 3.

然后，由于 num大于0，因此会再次调用factorial，不过这次是计算 3 的阶乘了。

2.What happens, for instance, if you try to find the value of the factorial of 4? Let's follow the sequence

例如，如果我们要计算4的阶乘为多少，到底会发生什么呢？

3.The same method to calculate the factorial, this time written for the Duby compiler.

下面同样是计算阶乘的方法，这次是针对Duby编译器而写的。

4.We only use it the first time we call fact, at the end of factorial.

我们只在第一次调用fact的时候需要它，也就是在factorial的最后。

5.Now, in the new call to factorial, num is set to 3.

现在，在新一次调用factorial时，num被设置为3。

6.Now, invoke the next factorial.

现在，调用下一个factorial。

7.This limits greatly the possible range of your factorial function.

这极大地限制了阶乘函数的可能范围。

8.The recursive C code is return num * factorial(num - 1).

递归的C代码是returnnum *factorial(num-1)。

9.In mathematics, the factorial (阶乘) of a non-negative integer n is the product of all positive integers less than or equal to n.

在数学中，非负整数 n 的 factorial (阶乘) 是小于或等于 n 的所有正整数的乘积。

10.The calculation of factorial (阶乘) is essential in combinatorics for determining permutations and combinations.

在组合数学中，计算 factorial (阶乘) 对于确定排列和组合是至关重要的。

11.To find the number of ways to arrange 5 books on a shelf, you would calculate 5!, which is 120, using the factorial (阶乘) function.

要找出将 5 本书排列在书架上的方法数量，你需要计算 5!，即 120，使用 factorial (阶乘) 函数。

12.In programming, many languages provide built-in functions to compute the factorial (阶乘) of a number efficiently.

在编程中，许多语言提供内置函数来高效计算一个数字的 factorial (阶乘)。

13.The factorial (阶乘) of 0 is defined to be 1, which is a unique property in mathematics.

0 的 factorial (阶乘) 被定义为 1，这是数学中的一个独特属性。

作文

The concept of factorial is fundamental in mathematics, particularly in the fields of combinatorics and probability. The factorial of a non-negative integer n, denoted as n!, is defined as the product of all positive integers less than or equal to n. For instance, the factorial of 5, written as 5!, is calculated as 5 × 4 × 3 × 2 × 1, which equals 120. Understanding factorial is essential for anyone interested in mathematics, as it lays the groundwork for more complex concepts such as permutations and combinations. In practical terms, factorial is used to determine the number of ways to arrange a set of objects. For example, if you have three books and you want to know how many different ways you can arrange them on a shelf, you would calculate the factorial of 3. This is because the first book can be any of the three, the second book can be any of the remaining two, and the last book has only one choice left. Therefore, the calculation would be 3! = 3 × 2 × 1 = 6. Thus, there are six possible arrangements of the three books. Moreover, factorial finds applications beyond simple arrangements. In statistics, it plays a crucial role in calculating probabilities. For example, when determining the likelihood of certain outcomes in a random experiment, the factorial function helps in computing combinations. The number of ways to choose k items from a set of n items is given by the formula n! / (k!(n-k)!), where both n and k are non-negative integers. This formula is pivotal in various fields such as genetics, finance, and science, where understanding the likelihood of different combinations is vital. Another interesting aspect of factorial is its rapid growth. As n increases, n! grows exponentially, which can lead to very large numbers even for relatively small values of n. For example, 10! equals 3,628,800, while 20! is a staggering 2,432,902,008,176,640,000. This explosive growth can pose challenges when performing calculations, especially in computer programming and algorithm design, where handling large integers efficiently is necessary. Therefore, mathematicians and computer scientists often use approximations like Stirling's approximation to estimate factorial values without computing them directly. In conclusion, the factorial function is a powerful mathematical tool that serves various purposes across different disciplines. Whether you are arranging objects, calculating probabilities, or analyzing data, understanding factorial is crucial. Its significance extends beyond theoretical mathematics into real-world applications, making it an essential concept for students and professionals alike. By mastering the principles of factorial, individuals can enhance their analytical skills and apply these concepts effectively in diverse scenarios.

“阶乘”这个概念在数学中是基础性的，尤其是在组合数学和概率论领域。非负整数n的阶乘，记作n!，定义为所有小于或等于n的正整数的乘积。例如，5的阶乘，即5!，计算为5 × 4 × 3 × 2 × 1，结果为120。理解阶乘对于任何对数学感兴趣的人来说都是必不可少的，因为它为更复杂的概念如排列和组合奠定了基础。 在实际应用中，阶乘用于确定一组对象的排列方式。例如，如果你有三本书，想知道可以用多少种不同的方式将它们排列在书架上，你会计算3的阶乘。这是因为第一本书可以是三本中的任意一本，第二本书可以是剩下的两本中的任意一本，最后一本书只有一个选择。因此，计算为3! = 3 × 2 × 1 = 6。因此，这三本书可以有六种可能的排列方式。 此外，阶乘在统计学中也发挥着关键作用，帮助计算概率。例如，在确定随机实验中某些结果的可能性时，阶乘函数有助于计算组合。从n个项目中选择k个项目的方法数量由公式n! / (k!(n-k)!)给出，其中n和k都是非负整数。这个公式在遗传学、金融和科学等各个领域中至关重要，在这些领域中，理解不同组合的可能性是非常重要的。 阶乘的另一个有趣方面是它的快速增长。随着n的增加，n!呈指数级增长，这甚至对于相对较小的n值也会导致非常大的数字。例如，10!等于3,628,800，而20!是惊人的2,432,902,008,176,640,000。这种爆炸式增长在进行计算时可能会带来挑战，尤其是在计算机编程和算法设计中，处理大整数的效率至关重要。因此，数学家和计算机科学家通常使用斯特林近似法来估计阶乘值，而无需直接计算它们。 总之，阶乘函数是一种强大的数学工具，在不同学科中服务于多种目的。无论是排列对象、计算概率还是分析数据，理解阶乘都是至关重要的。它的重要性超越了理论数学，延伸到现实世界的应用，使其成为学生和专业人士的基本概念。通过掌握阶乘的原理，个人可以增强他们的分析能力，并在各种场景中有效地应用这些概念。