is the number of bits which would have to be transmitted to identify X from N equally likely possibilities, less the relative entropy of the uniform distribution on the random variates of X, P U ( X ) , from the true distribution P ( X ) — i.e. less the expected number of bits saved, which would have had to be sent if the value of X were coded according to the uniform distribution P U ( X ) rather than the true distribution P ( X ) . This definition of Shannon entropy forms the basis of E.T. Jaynes 's alternative generalization to continuous distributions, the limiting density of discrete points (as opposed to the usual differential entropy), which defines the continuous entropy as