Is an "infinitely sharp blade" possible? A staple of science fiction and fantasy is a blade (knife, sword, ...) that cuts through literally any solid object (wood, steel, concrete, skulls, ...) without effort, often even without the need to apply any pressure.
What (in theory) would be required to construct such a blade? Would, say, a diamond wedge that is only a single atom thick on one side have that property? Or is it physically impossible to make such a blade? If yes, what is the limiting factor?
 A: Pressure is a measure of the force applied to a given area. Blades are sharp because they have a small cross sectional area, allowing you to create very high pressure whilst applying only a modest force. This force generates so much of shear stress on the object getting cut that it crushes through the molecular bonds in that object. Cutting through something can tear its molecules apart but it does nothing to the atoms of that object.
A blade which is a single atom thick would firstly not be sturdy. Even if it was, it would get dull in a matter of seconds and will also be highly unstable (if it's metal).
A: A blade must be near-atomically thin to generate immense local pressures to cleave "anything."  The edge must also be immensely stiff to avoid contact deformation.  The brittle edge could be mounted in a tough matrix to avoid brittle failure, or erode as it cut to maintain its edge (e.g., pattern-welded Samurai/Damascus steels, Talonite; uranium long rod penetrators).
However, diamond phonograph needles dulled rubbing against vinyl phonograph records.  Fluted diamond micro end mills dull cutting Plexiglas (cutting intraocular lenses from rod or sheet stock).  Physical erosion is accompanied by chemical erosion.  Being hard won't save you there.
If you could fabricate a cubic boron nitride-dispersed cutting edge (diamond is unstable in hot ferrous alloys to catalyzed conversion into graphite) in the manner of Samurai steel, it could be interesting.  Remember that the trace vanadium that does the magic for precipitating fern-like flat plates of iron carbides.  c-BN is grit.
The only reasonable reduction to practice is then a non-material edge constantly renewing itself microsecond to microsecond.  An ${Ar_2}$* excimer laser is 126 nm (9.9 eV/photon), a ${Ne_2}$* excimer laser is 88 nm (14.1.eV/photon).  A chemical bond tops off around 3 eV.  Go for it.
A: Such a blade (zero pressure required to cut a solid material) is not achievable. Even if you can produce an indefinitely thin edge, the body of the blade still has to force the sides of the cut apart. Think of cutting a steel block which is, say, one inch thick. Let's say that the blade is 1/2 inch deep with a back edge 1/8 of an inch wide. When you've cut half way through the block, the back edge of the blade will need to deform the top surface of the block by 1/8 of an inch, and this will be resisted by the 1/2 inch of the block still unaffected.
A: I think that no blade made of atomic matter (not degenrated matter) would be able to cut through everything else (like neutron star for example). As for a blade made from degenrate matter I also think that it would not be possible, because it takes huge amounts of force to keep matter stable in such form.
A: Not possible, because if you want a very sharp blade, it should be very thin. On the other hand, cut material into two parts need to break the chemical bond of the molecules. However the blade is too thin that even if it cut off the bond(rather than saying get through), the bond will form again.
