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It is similar to cartesian product of sets $\{a,b\} \times \{c,d\} = \{(a,c), (a,d), (b,c), (b,d)\}$, but applied to (ordered) tuples and without the permutations that don't match, i.e. $\langle a,b\rangle zip \langle c,d\rangle = \langle(a,c), (b,d)\rangle$.

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    $\begingroup$ If $(c, d)=(a, b)$ this is called the diagonal of $(a, b)\times (a, b)$ and is often denoted by $\Delta$ or $\Delta_{(a, b)}$ (or similar things involving $\Delta$). If you specify what you mean by "$\mathrm{zip}$", you can use $(a, b)\,\mathrm{zip}\,(c, d)$, too. It's a perfectly fine piece of notation. $\endgroup$ Aug 28, 2019 at 22:05

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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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A $n$-tuple is a function with $n$ (a canonical set of $n$ elements, typically $\{0,1,\ldots,n-1\}$) as its domain.

So if we have two $n$-tuples $f,g$, we can take the so-called diagonal product $f \nabla g$ defined on $n$ by $(f \nabla g)(n) = (f(n), g(n))$. This comes close to your zip function. If we have different domains $n$ and $m$ we can only define it on $\min(n,m)$ etc.

There are more notations for diagonal product I think, but this is one that is used in topology sometimes.

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