Mankind has been putting sharp edges on rocks or metals for well over 100,000 years, so it is not surprising that we have learned to embellish edged items with values that go well beyond utilitarian usage. We do this with all kinds of stuff.

When it comes to sharpening, the sharpest possible edge is produced by flaking off a chip from a piece of obsidian (volcanic glass), its more common modern day equivalent, the bottom of a glass beer bottle. The edge will not last long, but it is about a molecule wide at the tip, which is pretty darn thin. Not very expensive, either.