limit of a real sequence

数列极限

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

Translation evidence: Literature usage

Meaning in context

A real sequence has limit a if, for every positive epsilon, all terms beyond some index lie within epsilon of a.

实数列以 a 为极限，是指任给正误差，存在一个指标，使其后所有项与 a 的距离都小于该误差。

Example

$a_n=2+1/n$ tends to $2$.

Usage and distinctions

A finite limit differs from divergence to positive infinity.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Michael Taylor — Introduction to Analysis in One Variable§1.5 Sequences · Checked 2026-10-14

Translation sources

1. 中国矿业大学数学学院 — 数学分析讲义，第二章§1 数列极限的概念, 定义1 · Checked 2026-10-14

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