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绝对值 定义

The absolute value or modulus of a real number x, denoted |x|, is the non-negative value of x without regard to its sign. Namely, |x| = x if x is positive, and |x| = −x if x is negative (in which case −x is positive), and |0| = 0. For example, the absolute value of 3 is 3, and the absolute value of −3 is also 3. Essentially, absolute value turns all negative numbers positive and leaves positive numbers and zero unchanged. The absolute value of a number may be thought of as its distance from zero.

数字的绝对值是数字与origin 之间的距离。这是绝对值的更精确定义，因为它将绝对值的概念与复数的绝对值 和向量的大小 联系起来。实数的绝对值的推广出现在各种各样的数学设置中。例如，还为复数、四元数、有序环、域和向量空间定义了一个绝对值。绝对值与各种数学和物理上下文中的 magnitude、距离和 norm 的概念密切相关。