real number

简明释义

实数

英英释义

例句

1.The set of real numbers 实数 includes both rational and irrational numbers.

实数的集合包括有理数和无理数。

2.You can find the real number 实数 by using a graphing calculator.

你可以使用图形计算器找到这个实数。

3.In mathematics, a real number 实数 can be either positive or negative.

在数学中，实数可以是正数或负数。

4.The solution to the equation is not a real number 实数, but an imaginary one.

这个方程的解不是一个实数，而是一个虚数。

5.Every integer is a real number 实数, but not every real number 实数 is an integer.

每个整数都是一个实数，但不是每个实数都是整数。

作文

In mathematics, the concept of a real number is fundamental. A real number can be defined as any value that represents a quantity along a continuous line, which includes both rational and irrational numbers. Rational numbers are those that can be expressed as a fraction of two integers, such as 1/2 or -3. On the other hand, irrational numbers cannot be expressed as simple fractions; examples include the square root of 2 and the number pi (π). Understanding real numbers is crucial not only in pure mathematics but also in various applications across other fields such as physics, engineering, and economics.The set of real numbers is often denoted by the symbol R. This set encompasses all the numbers that can be found on the number line, extending infinitely in both the positive and negative directions. One of the most interesting properties of real numbers is that they can be used to represent quantities that we encounter in everyday life. For instance, when measuring the height of a person, the temperature outside, or even the distance between two cities, we use real numbers to convey these measurements accurately.Moreover, real numbers are essential when it comes to performing calculations. In algebra, we frequently manipulate real numbers to solve equations, analyze functions, and explore mathematical relationships. The ability to perform operations such as addition, subtraction, multiplication, and division with real numbers allows us to tackle complex problems and derive meaningful conclusions.One significant aspect of real numbers is their density. Between any two real numbers, there exists another real number. This property implies that there are infinitely many real numbers between any two given values, no matter how close they are to each other. This characteristic is particularly important in calculus, where limits and continuity are examined.Furthermore, real numbers can be classified into different categories based on their properties. For example, we have positive real numbers, negative real numbers, and zero. Each category plays a unique role in various mathematical contexts. Positive real numbers are often associated with quantities greater than zero, while negative real numbers represent values less than zero. Zero itself is a special real number that serves as the additive identity in arithmetic, meaning that adding zero to any real number does not change its value.In conclusion, the concept of real numbers is integral to mathematics and its applications. From simple calculations in everyday life to complex theories in advanced mathematics, real numbers provide a framework for understanding and describing the world around us. Mastering the properties and operations involving real numbers is essential for students and professionals alike, as it lays the groundwork for further studies in mathematics and related fields. Therefore, taking the time to fully grasp the significance of real numbers will undoubtedly enhance one’s mathematical literacy and problem-solving skills.

在数学中，实数的概念是基础性的。实数可以被定义为任何代表沿连续线的数量的值，包括有理数和无理数。有理数是那些可以表示为两个整数之比的数，例如1/2或-3。另一方面，无理数则不能简单地表示为分数；例如，2的平方根和圆周率(π)就是无理数。理解实数不仅在纯数学中至关重要，而且在物理、工程和经济等其他领域的各种应用中也同样重要。实数的集合通常用符号R表示。这个集合包含了所有可以在数轴上找到的数字，向正方向和负方向无限延伸。实数的一个有趣特性是它们可以用来表示我们日常生活中遇到的数量。例如，在测量一个人的身高、外面的温度，甚至是两个城市之间的距离时，我们使用实数来准确传达这些测量值。此外，实数在进行计算时也是必不可少的。在代数中，我们经常操纵实数来解方程、分析函数和探索数学关系。能够对实数进行加法、减法、乘法和除法等运算，使我们能够解决复杂的问题并得出有意义的结论。实数的一个重要方面是它们的密度。在任何两个实数之间，都存在另一个实数。这个特性意味着在任意两个给定值之间都有无限多个实数，无论它们彼此多么接近。这一特性在微积分中特别重要，因为在微积分中研究极限和连续性。此外，实数可以根据其属性分为不同的类别。例如，我们有正实数、负实数和零。每个类别在各种数学背景中都扮演着独特的角色。正实数通常与大于零的数量相关，而负实数则表示小于零的值。零本身是一个特殊的实数，在算术中作为加法单位，这意味着将零加到任何实数上不会改变其值。总之，实数的概念对于数学及其应用至关重要。从日常生活中的简单计算到高级数学中的复杂理论，实数为理解和描述我们周围的世界提供了框架。掌握涉及实数的属性和运算对于学生和专业人士来说都是必不可少的，因为这为进一步研究数学和相关领域奠定了基础。因此，花时间充分理解实数的重要性无疑会增强一个人的数学素养和解决问题的能力。