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    How on earth would you show all the rectangles with length x metres and width y metres, with x and y being natural numbers as denumerable?

    (0,0), (1,0)
    (0,0), (1,0) ??

    I honestly have no idea so some help would be really good.

    Similarly, with letters and strings of them, to show they are denumerable would be something like this:

    0, 1, 2, 3
    a, b, ab, ba


    I think your question is: Prove \mathbb{N}^2 is countable. There are many ways to do this, for instance, consider this visually as points in the first quadrant and "join the dots" in a natural way.

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