absolute value

简明释义

绝对值

英英释义

例句

1.The function returns the absolute value of the input.

该函数返回输入的绝对值。

2.In mathematics, the absolute value is defined as the distance from zero.

在数学中，绝对值被定义为与零的距离。

3.The absolute value of 3.14 is 3.14.

3.14的绝对值是3.14。

4.To find the absolute value of a number, you ignore its sign.

要找出一个数字的绝对值，你需要忽略它的符号。

5.The absolute value of -5 is 5.

负数-5的绝对值是5。

作文

The concept of absolute value is fundamental in mathematics, particularly in the study of numbers and their properties. The absolute value of a number refers to its distance from zero on the number line, regardless of direction. This means that both positive and negative numbers have the same absolute value. For example, the absolute value of -5 is 5, and the absolute value of 5 is also 5. Therefore, we can conclude that absolute value is always non-negative.Understanding the absolute value is not only crucial for basic arithmetic but also plays a significant role in various mathematical fields such as algebra, calculus, and even complex numbers. In algebra, when solving equations, we often encounter expressions involving absolute value. For instance, if we have the equation |x| = 3, it implies that x can be either 3 or -3. This duality reflects how absolute value encapsulates the idea of magnitude without regard to sign.Moreover, the absolute value function can be visualized graphically. When plotted on a coordinate plane, the graph of the absolute value function y = |x| creates a V shape. This V shape indicates that as x moves away from zero in either direction, y increases, demonstrating the non-negative nature of absolute value. The vertex of this graph is at the origin (0,0), which signifies that the absolute value of zero is zero itself.In real-world applications, the absolute value concept is used in various fields such as physics, engineering, and computer science. For instance, in physics, when calculating the displacement of an object, we often need to consider the absolute value of the distance traveled, as the direction may not always be relevant. Similarly, in engineering, when assessing tolerances and deviations in measurements, the absolute value allows engineers to determine how far off a measurement is from a desired value, irrespective of whether it is over or under the target.Furthermore, the notion of absolute value extends beyond numbers into the realm of functions and vectors. In vector mathematics, the absolute value, often referred to as the magnitude of a vector, represents its length. This is calculated using the Pythagorean theorem, where the magnitude of a vector with components (x, y) is given by √(x² + y²). This application of absolute value highlights its versatility across different branches of mathematics.In conclusion, the absolute value is a powerful mathematical tool that simplifies our understanding of numbers and their relationships. By focusing on the magnitude rather than the sign, we can solve problems more efficiently and apply these concepts in various practical scenarios. Whether in pure mathematics or applied sciences, mastering the concept of absolute value is essential for anyone looking to enhance their mathematical literacy and problem-solving skills. As we continue to explore the vast world of mathematics, the absolute value will remain a cornerstone of our understanding, guiding us through complex equations and real-world challenges.

绝对值的概念在数学中是基础，特别是在数字及其性质的研究中。一个数字的绝对值指的是它与零在数轴上的距离，无论方向如何。这意味着正数和负数具有相同的绝对值。例如，-5的绝对值是5，而5的绝对值也是5。因此，我们可以得出结论：绝对值始终是非负的。理解绝对值不仅对基本算术至关重要，还在代数、微积分甚至复数等各种数学领域中发挥着重要作用。在代数中，当我们解方程时，常常会遇到涉及绝对值的表达式。例如，如果我们有方程|x| = 3，这意味着x可以是3或-3。这种双重性反映了绝对值如何包含不考虑符号的大小的概念。此外，绝对值函数可以通过图形可视化。当在坐标平面上绘制时，绝对值函数y = |x|的图形创建一个V形。这种V形表明，随着x朝任一方向远离零，y增加，展示了绝对值的非负特性。该图形的顶点位于原点（0,0），这表明零的绝对值也是零。在现实世界的应用中，绝对值概念被广泛用于物理、工程和计算机科学等各个领域。例如，在物理学中，当计算物体的位移时，我们常常需要考虑行驶距离的绝对值，因为方向可能并不总是相关。同样，在工程中，当评估测量中的公差和偏差时，绝对值使工程师能够确定测量值与目标值的偏差，无论是超出还是低于目标。此外，绝对值的概念超越了数字，延伸到函数和向量的领域。在向量数学中，绝对值，通常称为向量的大小，表示其长度。这是使用勾股定理计算的，其中具有分量（x，y）的向量的大小由√(x² + y²)给出。这种绝对值的应用突显了它在不同数学分支中的多功能性。总之，绝对值是一个强大的数学工具，它简化了我们对数字及其关系的理解。通过关注大小而不是符号，我们可以更有效地解决问题，并在各种实际场景中应用这些概念。无论是在纯数学还是应用科学中，掌握绝对值的概念对于任何希望提高数学素养和解决问题能力的人都是必不可少的。随着我们继续探索广阔的数学世界，绝对值将始终是我们理解的基石，引导我们通过复杂的方程和现实挑战。