function between sets

映射

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

Other names / variants: function

Translation evidence: Literature usage

Meaning in context

For specified sets A and B, an assignment giving each member of A exactly one member of B.

对于指定的集合 A、B，为 A 的每个元素指定 B 中唯一一个元素的对应。

Example

n↦n+2n\mapsto n+2 defines a map Z→Z\mathbb Z\to\mathbb Z.

Usage and distinctions

A formula alone does not specify a function until domain and codomain are stated.

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. 李文威 — 代数学方法，第一卷（作者源码）第1章：「ZFC 公理一览」，配对公理后的映射图形段 · Checked 2026-10-14
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