  The Bell and Wigner inequalities are commonly derived using logically
separate procedures.It is not generally appreciated that they are closely
related.Their relationship follows from the fact that the Bell inequality
describes a constraint on the correlations of random variable pairs and leads
to a constraint on the probabilities from which they are computed.In the case
of the Bell inequality, the logic of the constraint is further clarified when
it is found that the inequality that Bell derived for correlation functions
must be identically satisfied by the data sets of +-1s used to compute the
correlations.This data set inequality is independent of the assumptions used by
Bell in the course of derivation of the correlation inequality.Thus, the Bell
inequality in its most fundamental form cannot be violated by the number of
data sets used in deriving it regardless of their individual
characteristics.When the Bell inequality is applied to three predicted
correlations using properties based on perfect entanglement, the resulting
symmetries allow correlations to be replaced by their probabilities in the
inequality.The Wigner inequality follows.The two related inequalities are
satisfied by correlations and probabilities respectively computed using quantum
mechanical principles.
