Harmonic entropy: Difference between revisions
add zeta stuff -- still unfinished, will try to add pictures tomorrow |
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All of the models described above involve a finite set of rational numbers, bounded by some complexity function, and where the complexity is less than some max value <math>N</math>. | All of the models described above involve a finite set of rational numbers, bounded by some complexity function, and where the complexity is less than some max value <math>N</math>. | ||
It so happens that we are able to analytically continue this definition to the situation where <math>N=\infty</math>, | It so happens that, with one technical caveat, we are generally able to analytically continue this definition to the situation where <math>N=\infty</math>. More precisely, we are able to analytically continue the exponential of HE, which yields the same relative interval rankings as standard HE. | ||
This enables us to speak cognizantly of the harmonic entropy of an interval as measured against ''all'' rational numbers. | |||
==Background: Unnormalized Entropy== | ==Background: Unnormalized Entropy== | ||