(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Given two sets of Cartesian product

S=A_{1}×A_{2}...×A_{n}

P=(A_{1}×A_{2}...×A_{n-1})×A_{n}

show that there exists bijection between the two sets.

2. Relevant equations

∀a_{1},a_{2}:a_{1}∈A_{1}, a_{2}∈A_{2}: A_{1}×A_{2}=(a_{1},a_{2})

3. The attempt at a solution

let f be a function that maps

f: P → A_{1}×A_{2}...×A_{n-1}where f((A_{1}×A_{2}...×A_{n-1}))∈A_{1}×A_{2}...×A_{n-1}and f(A_{n})∈A_{n}

is this correct?

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# Homework Help: Cartesian Product and Bijection

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