# Multiplication of cardinal numbers

Let $a_i$ be a cardinal number for every $i \in\ I$.

Let $\{A_i\}$ and $\{A'_i\}$ be families of sets and let $A_i$, $A'_i$ and $a_i$ be equipotent for every $i \in I$.

Then show that $\prod_i\ A_i $ is equipotent with $\prod_i\ A'_i $.

This seems obviously true but I don't know how to actually show the bijection between them..

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Katlus 2022-07-25 20:41:54

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