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The set of all possible submarine routes is countable (velocity vector + position at time 0). Let's assume we have an enumeration of that set. Now it's easy to bomb them all. At time 1 we bomb the point where submarine 1 is at time 1, at time 2 we bomb the point where submarine 2 is at time 2, and so on.

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Yep, this is how the proof works!

How does that use the diagonal argument? If the diagonal argument could be used it would be to prove that the number of submarine routes isn't countable.

Edit: just looked at the SVG called "Diagonal Argument.svg". That's not what I know as the diagonal argument (https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument, http://mathworld.wolfram.com/CantorDiagonalMethod.html)

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