 With these terms in place it is easy to show that if, say, the values of position and momentum for a quantum system were definite (were elements of reality) then the description provided by the wave function of the system would be incomplete, since no wave function contains counterparts for both elements. Technically, no state function—even an improper one, like a delta function—is a simultaneous eigenstate for both position and momentum; indeed, joint probabilities for position and momentum are not well-defined in any quantum state. Thus they establish the first premise: either quantum theory is incomplete or there can be no simultaneously real (“definite”) values for incompatible quantities. They now need to show that if quantum mechanics were complete, then incompatible quantities could have simultaneous real values, which is the second premise. This, however, is not easily established. Indeed what EPR proceed to do is odd. Instead of assuming completeness and on that basis deriving that incompatible quantities can have real values simultaneously, they simply set out to derive the latter assertion without any completeness assumption at all. This “derivation” turns out to be the heart of the paper and its most controversial part. It attempts to show that in certain circumstances a quantum system can have simultaneous values for incompatible quantities (once again, for position and momentum), where these are definite values; that is, they are assigned by the real state of the system, hence are “elements of reality”.