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台阶不连续 定义
A step discontinuity or jump discontinuity is a discontinuity where the graph steps or jumps from one connected piece of the graph to another. It is a discontinuity where the limits from the left and right both exist but are not equal to each other. A real-valued univariate function f = f(x) has a step discontinuity at a point x0 in its domain provided that limx→xa- f(x) = L1 < ∞, and limx→xa+ f(x) = L1 < ∞. both exist and L1 ≠ L2.
阶梯不连续的概念不应与很少使用的约定相混淆,其中术语 jump 用于定义任何类型的功能不连续。虽然没有 可移动间断 在代数上不那么简单,但阶梯间断远不如其他类型的奇点(例如无限间断)表现不佳。在许多情况下都可以看到这一事实。例如,univariate 单调函数最多可以有许多不连续性,其中最严重的可能是阶跃不连续性。不出所料,上面给出的定义也可以推广到 multivariate 实值函数中的阶跃不连续性。
来源
“Jump Discontinuity.” From Wolfram MathWorld, mathworld.wolfram.com/JumpDiscontinuity.html.