bijective function

双射

Foundations & Logic · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Other names / variants: bijection · 一一对应

Translation evidence: Literature usage

Meaning in context

A function that is both injective and surjective, equivalently one admitting a two-sided inverse.

既单又满的映射；等价地，具有左右两侧逆映射的映射。

Example

n↦−nn\mapsto-n is a bijection Z→Z\mathbb Z\to\mathbb Z.

Usage and distinctions

An inverse relation becomes an inverse function on the entire codomain only for a bijection.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Avigad, Hua, Lewis and van Doorn — Logic and Proof§15.1 The Function Concept; §15.2 Injective, Surjective, and Bijective Functions; §15.3 Functions and Subsets of the Domain · Checked 2026-10-14

Translation sources

  1. 高等教育出版社 — 数学证明 通往高等数学的阶梯（第4版）影印版，官方中文目录官方中文目录：§10.3 双射函数（名称证据，非正文定义证据） · Checked 2026-10-14
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