injective function

单射

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

Other names / variants: injection

Translation evidence: Literature usage

Meaning in context

A function f:A→Bf:A\to B for which f(x)=f(y)f(x)=f(y) implies x=yx=y for all x,y∈Ax,y\in A.

对所有定义域元素 x、y，f(x)=f(y) 都推出 x=y 的映射。

Example

n↦5nn\mapsto5n is an injection Z→Z\mathbb Z\to\mathbb Z.

Usage and distinctions

Injectivity prohibits collisions; it does not require covering the codomain.

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：§10.2 单射函数与满射函数（名称证据，非正文定义证据） · Checked 2026-10-14
Edit source / propose a PRReport a correction

Original encyclopedia and terminology content: CC BY-SA 4.0. Contribute or report a correction.