Suppose you introduce a boundary by separating one piece of a continuum from another. By hypothesis, we are now at least treating the continuum as digital, which means the border must be
somewhere. That is, there must be some piece of the continuum that is on one side of the border, and another piece on the other side (or at least, we treat things this way). And there must be
no distance between these two points, or else the border itself will have distance, and the question of the digitalization of how long the border is then just repeats the problem whole again. But then, the only way for this to happen is if we can identify two discrete pieces of the continuum, and say that one is on one side, the other on the other. So for any piece of the continuum, once the boundary is there, we can say definitively which side it's on, and as a result there now is, or at least we take there to be, an absolutely discrete cutoff between one side of the boundary or the other.
But where is that boundary? How can we tell, in virtue of placing the boundary? How can we tell where we've put the boundary at all? One way is to say, we just look at which things fall on either side of it: but this begs the question, since if we could determine precisely to begin with, before knowing where the boundary is set, which side each was on, then there will have
ipso facto been digitalized distinctions between those two things that lie on opposite sides of the border all along, since we need to make this digitalization
in order to place the border. But if we do not assume this, then we have no reason to say that the border was placed at once place rather than another, and we literally cannot figure out exactly where it is, or which things digitally fall on either side of it, hence the border itself becomes analog, and contrary to hypothesis we have done no digitalizing in placing the border.