How to draw the cartesian product of two infinite sets?

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If I have sets A and B with the cardinality of the set of Integers, making these sets denuermable sets by definition, how could they be drawn?

I have a rough idea as it would look like ordered pairs, just like a coordnate for a 2D grid, inside a little box surrounded by multiple boxes going in all directions holding different ordered pairs.

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List A as $a_1, a_2, a_3, ...$ and B as $b_1, b_2, b_3, ....$

Place for all positive integers k, $a_k$ on (k,0) and $b_k$ on (0,k).
You will see A laided out as positive integers on the x-axis
and B laided out as positive integers on the x-axis.

Consequently you'll see AxB laided out as all the
points (n,m) on the plane with positive integers n,m.