In fact, the limit of discrete entropy as N → ∞ {\displaystyle N\rightarrow \infty } would also include a term of log ⁡ ( N ) {\displaystyle \log(N)} , which would in general be infinite. This is expected, continuous variables would typically have infinite entropy when discretized. The limiting density of discrete points is really a measure of how much easier a distribution is to describe than a distribution that is uniform over its quantization scheme.