In theory, sure, though of course in practice they are treated differently. Wedges take positive advantage of characteristics that would cause poor knife performance.
(The words even show it - if you get your knife “wedged” in the material you’re cutting, something has probably gone wrong.)
Indeed but I am willing to bet you know that ancient Greeks weren’t really up on their physics and did not know there are smaller things than atoms.
As to the OP I think it has been covered here but I will add a molecule thick cutting surface is not likely to last long. Since it is so thin it will start to abrade away almost as soon as you start cutting.
But yeah…for that first cut it will be mighty sharp but that single molecule thickness will disappear almost as soon as you start cutting. It will remain mighty sharp for a bit but it will probably dull quickly to more “normal” sharpness (which is still sharp).
Death’s scythe is one of the two sharpest objects in existence. It is capable of slicing air, shadows and even time. Most importantly, it is designed to sever souls from their mortal shells. The blade is almost transparent, but glows blue thanks to the energy released by atoms splitting on its edge (thanks to the idiosyncrasies of Discworld physics, this does not cause the nuclear obliteration of a vast area).
in the Volsunga Saga, Sigurd’s sword Gram was tested first by cutting an anvil in half, then by throwing wool upstream and dipping the sword into the stream and letting the wool drift down and be cut by the edge. Cite.
I sympathize with Regin the dwarf smith, but that’s what you get when you let the users write the specs document.
What started my BS flag flapping was the conditions of the find itself. If it ever had an edge of one molecule dimension, what are the chances that it would remain intact through thousands of years of exposure to the environment? The more so, when it is fashioned of organic composition. Although, a diamond is also organic, so that may not be germane.
Many surgeons use obsidian scalpels. They’re demonstrably sharper than steel scalpels.
If there were something sharper than that, I’d imagine they’d use them.
ETA: Of course, this is just a legend; the two swordsmiths weren’t even contemporaries (about 300 years separated them, which is a little time in Japanese history). But that’s the legend, incorporating the cultural memes associated with the two foremost swordsmiths in Japanese history: Masamune made holy swords, and Muramasa made evil and blood-thirst swords.
I’ve also heard a version of that story where Masamune’s blade didn’t even cut the leaves, but parted the water around it so that there would be no unnecessary destruction at all.