jump discontinuity

跳跃间断点

Analysis, Measure & PDE · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Translation evidence: Literature usage

Meaning in context

A real function has a jump at a when both finite one-sided limits exist and are unequal.

实函数在 a 处左右极限都存在且有限、但不相等，则 a 为跳跃间断点。

Example

1[0,∞)\mathbf1_{[0,\infty)} jumps from 00 to 11 at 00.

Usage and distinctions

Changing the value at a cannot make unequal side limits agree.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Michael Taylor — Introduction to Analysis in One Variable§3.1, continuity and limits · Checked 2026-10-14
  2. OpenStax — Calculus Volume 1§2.4, Types of Discontinuities, Definition item 2 (jump discontinuity) · Checked 2026-10-15

Translation sources

  1. 中国矿业大学数学学院 — 数学分析讲义，第四章§1 二、间断点的分类, 2 跳跃间断点 · Checked 2026-10-14
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