Glossary math Term Page

Bijection

A perfect one-to-one and onto matching between two sets

bijection #math#set-theory

Aliases

bijectionone-to-one correspondence

Prerequisites

Function (math)

Related Concepts

Function (math)Injective function Surjective function Cardinality

Core Idea

A bijection is a function that is both injective and surjective. It matches two sets with no overlaps and no leftovers.

Role In This Blog

In Mathbong, bijection is the main tool for comparing set sizes, especially when infinite sets enter the discussion.

Posts Mentioning This Concept

[Set Theory Series 7] Functions: From Relations to Functions Understand functions as a special kind of relation, and organize domain, codomain, image, injective, surjective, and bijective ideas.[집합론 시리즈 7편] 함수: 관계에서 함수로 함수를 특별한 관계로 이해하고, 정의역·공역·치역과 일대일·전사·전단사를 함께 정리합니다.[Set Theory Series 8] Cardinality and the Basics of Infinity Start from the size of finite sets and build the first intuition for comparing infinite sets through bijections.