subsequence of a real sequence

子列

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

Translation evidence: Literature usage

Meaning in context

A subsequence of (a_n) is (a_{n_k}) where the positive integer indices n_k increase strictly.

从实数列按严格递增的正整数指标抽取各项所组成的数列称为子列，原有次序必须保留。

Example

The even-index subsequence of (−1)n(-1)^n is constantly 11.

Usage and distinctions

Reordering terms arbitrarily does not define a subsequence.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Michael Taylor — Introduction to Analysis in One Variable§1.5 Sequences, subsequences · 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§2, 子列定义1, printed p.14 · Checked 2026-10-14
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