Like trying to cut an 8.5 x 11 piece of paper in half such that if it worked you’d get two pieces of 8.5 x 11 pieces of paper, but thinner? You’d just push the edge and not cut it (of course in my example, the paper would get scrunched up; but if you had an extremely thin piece of anything the same thickness as the edge of the knife, the knife couldn’t cut it edge to edge. If the knife were really sharp, you could probably slice diagonally through the thin object through the surface plane or shave off a bit of the plane.)
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