removable discontinuity

可去间断点

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

Translation evidence: Literature usage

Meaning in context

At an accumulation point a of a real domain, a finite punctured limit exists but the function is absent or has a different value at a.

在实定义域的聚点 a，函数的去心极限存在且有限，但 a 处未定义或函数值不等于该极限时，称 a 为可去间断点。

Example

f(x)=sin⁡(x)/xf(x)=\sin(x)/x for x≠0x\ne0 extends continuously with f(0)=1f(0)=1.

Usage and distinctions

A jump has unequal one-sided limits and cannot be repaired at one point.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Michael Taylor — Introduction to Analysis in One Variable§3.1, continuity criterion · Checked 2026-10-14
  2. OpenStax — Calculus Volume 1§2.4, Types of Discontinuities, Definition item 1 (removable 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, 1 可去间断点 · Checked 2026-10-14
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