or histogram. An interpretation of Theorem \[thm:universalAchievability\] is thus that histograms, from a certain class, with total weight $n$ can be encoded with $n + o(n)$ bits. Figure \[fig:histogram\] shows a histogram. An encoding method that shows the plausibility of $n + o(n)$ total rate is to encode the histogram one letter at a time, starting from the left end and moving to the right. After each letter, use [0]{} to indicate that there is another occurrence of the same letter and use [1]{} to move on to the next letter. If every symbol in the alphabet appears at least once, the rate is $n$; as long as the right-most letter encountered does not grow too quickly with $n$, an $n + o(n)$ rate is achieved.

Unattainability of Negligible Redundancy {#sec:Conv}
----------------------------------------

For finite alphabets, we showed that the multiset entropy rate is zero for any source; this is a crude consequence of Theorem \[thm:HRzero\]. We also saw, in the proof of Theorem \[thm:HRzero\], that simply enumerating the type classes requires zero rate per multiset letter asymptotically. Hence such a universal scheme requires zero rate for any finite-alphabet source. However, we cannot conclude from “zero equals zero” that the excess 