Name of $\{(1,1),(1,2),(1,3),(2,1),(2,2),(2,3),(3,1),(3,2),(3,3)\}$ in terms of $\{1,2,3\}$

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 $$A$$?

• It is the cartesian product $A \times A$ Apr 30 '20 at 12:49
• Just an afterthought, you could also say: $$B=\lbrace(x,y)|x,y\in A\rbrace$$ May 1 '20 at 1:16

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) $$A$$.