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This question is more about nomenclature than a problem to solve.

Imagine that I have a set

$$A = \{1,2,3\}$$

and I want do make the following set

$$B = \{(1,1),(1,2),(1,3),(2,1),(2,2),(2,3),(3,1),(3,2),(3,3)\}$$

How would I call the set $B$? Is this the set of all permutated pairs with all elements of $A$? But is this even permutations or combinations? How can I call $B$ in terms of $A$?

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    $\begingroup$ It is the cartesian product $A \times A$ $\endgroup$ Apr 30 '20 at 12:49
  • $\begingroup$ Just an afterthought, you could also say: $$B=\lbrace(x,y)|x,y\in A\rbrace$$ $\endgroup$ May 1 '20 at 1:16
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We can write this as $B = A\times A$, where $\times$ denotes the cartesian product. Alternatively, you might write $A^2$.

In words, you might say that $B$ is the set of all ordered pairs of (elements of) $A$.

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