  Einstein, Podolski and Rosen (EPR) have shown that any wave function (subject
to the Schr\"odinger equation) can describe the physical reality completely,
and any two observables associated to two non-commuting operators can have
simultaneous reality. In contrast, quantum theory claims that the wave function
can capture the physical reality completely, and the physical quantities
associated to two non-commuting operators cannot have simultaneous reality. The
above contradiction is known as the EPR paradox. Here, we unambiguously expose
that there is a hidden assumption made by EPR, which gives rise to this famous
paradox. Putting the assumption right this time leads us not to the paradox,
but only reinforces the correctness of the quantum theory. However, it is shown
here that the entanglement phenomenon between two physically separated
particles (they were entangled prior to separation) can only be proven to exist
with a "proper" measurement.
