How can I represent the (haskell, python etc.) zip function in math notation?

Given two families $(a_i\in A\mid i\in I)$ and $(b_i\in B\mid i\in I)$ with the same index set, the zip is a family $\left ((a_i,b_i)\in A\times B \mid i\in I\right)$

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Elementary Set Theory

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