factorials

简明释义

英[fæktəˌrɪəlz]美[fæktəˌrɪəlz]

n. [数]阶乘；[数]析因（factorial 的复数）

英英释义

单词用法

同义词

反义词

例句

1.Factorials design and Latin hypercube sampling design are applied in the high-speed milling experiments of martensitic stainless steel.

综合应用析因试验设计与拉丁超立方抽样试验设计，对难加工材料马氏体不锈钢进行了高速铣削试验。

2.Based on this analysis relationship, we propose the MPU rule, which can be used to compare two-level factorials.

之间的解析关系。基于这种解析关系，我们提出了一个用于比较二水平因子设计好坏的MPU准则。

3.The classic example of recursive programming involves computing factorials.

计算阶乘是递归程序设计的一个经典示例。

4.The Six Sigma Black Belt should know factorials, permutations and combinations, and how to use these in commonly used probability distributions.

六西格玛黑带应了解析因、置换、合并等方法，以及它们在概率分布中的一般应用。

5.The classic Haskell functions that you'll find in most tutorials are recursive math functions, such as Fibonacci functions and factorials.

在大多数教程中可以发现的大多数经典Haskell函数都是递归的数学函数，例如fibonacci函数和阶乘。

6.When factorials are needed they are read from the table.

当需要阶乘时，将从该表中读取阶乘。

7.How to use extended precision arithmetic to handle bigger factorials?

如何使用扩展精度运算处理更大的阶乘？

8.You can think of factorials in much the same way as Fibonacci sequences.

可以用与Fibonacci序列基本相同的方式对待阶乘。

9.In mathematics, we often use factorials to calculate permutations and combinations.

在数学中，我们经常使用阶乘来计算排列和组合。

10.The factorials of small numbers can be computed easily using a calculator.

小数字的阶乘可以通过计算器轻松计算。

11.To find the number of ways to arrange books on a shelf, you need to calculate the factorials of the total number of books.

要找到在书架上排列书籍的方式数量，您需要计算书籍总数的阶乘。

12.The formula for combinations involves factorials to determine how many groups can be formed.

组合的公式涉及阶乘以确定可以形成多少组。

13.When programming, understanding factorials is essential for algorithms that deal with combinatorial problems.

在编程时，理解阶乘对于处理组合问题的算法至关重要。

作文

Factorials are an essential concept in mathematics, particularly in the fields of combinatorics and probability. The notation for a factorial is represented by an exclamation mark. For example, the factorial of a number n, denoted as n!, is the product of all positive integers from 1 to n. This means that if we take the number 5, its factorial, written as 5!, would be calculated as 5 × 4 × 3 × 2 × 1, which equals 120. Understanding factorials (阶乘) is crucial because they help in calculating permutations and combinations, which are fundamental concepts in statistics. In combinatorics, factorials (阶乘) are used to determine the number of ways to arrange a set of objects. For instance, if we have three different books and we want to know how many different ways we can arrange them on a shelf, we would calculate this using factorials (阶乘). We would find that there are 3! = 3 × 2 × 1 = 6 different arrangements. This concept extends to larger sets of objects, making factorials (阶乘) a powerful tool in determining possible arrangements. Moreover, factorials (阶乘) play a significant role in probability theory. When calculating the probabilities of different outcomes, especially in scenarios involving multiple events, factorials (阶乘) are often employed. For instance, if we want to calculate the probability of drawing a specific sequence of cards from a deck, we can use factorials (阶乘) to determine the total number of possible sequences, which helps us find the desired probability. In addition to their applications in combinatorics and probability, factorials (阶乘) also appear in various mathematical formulas, including the binomial theorem and Taylor series expansion. These areas of study highlight the importance of factorials (阶乘) in higher-level mathematics, where they serve as building blocks for more complex equations. However, it is important to note that factorials (阶乘) grow very quickly as the numbers increase. For instance, while 5! equals 120, just one number higher, 6!, equals 720, and 7! jumps to 5040. This rapid growth can lead to large numbers that are difficult to manage, especially in computational contexts. As such, mathematicians and computer scientists often look for ways to simplify calculations involving factorials (阶乘), such as using approximations or logarithmic properties. In conclusion, factorials (阶乘) are a fundamental concept in mathematics with wide-ranging applications in combinatorics, probability, and beyond. They provide a method for quantifying arrangements and outcomes, making them invaluable tools for mathematicians, statisticians, and anyone working with data. As we continue to explore the world of mathematics, a firm grasp of factorials (阶乘) will undoubtedly enhance our understanding and ability to solve complex problems.