Yeah, 100%. There are (at least) two incorrect things the original commenter took for granted. First, that the infinite binary tree as he created it is equinu

Yeah, 100%. There are (at least) two incorrect things the original commenter took for granted. First, that the infinite binary tree as he created it is equinumerous with the natural numbers and therefore can stand in for the "list" in Cantor's diagonalization argument. Second, that a depth-first traversal of this tree makes sense. Your argument does a good job of showing why the first is a mistake. Assuming we can traverse it at all, it shouldn't matter whether we do so depth or breadth first. By traversing it breadth first we see clearly that we can always find a path through the three which does not correspond to any natural number, proving that the tree is not equinumerous with the naturals and, moreover, proving that there is an infinity which is "larger" than the infinity of the naturals.