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given the set ##\{r_i, r_{ii}, r_{iii}, ... , r_R\}##

where ##r \ \epsilon \ \mathbb{Z}_+ \ , \ r_i \geq r_{i+1}##

How would you go about finding the bounds of something like this, or determining if it even has any?

##( \, log_2{\frac{(\sum_{i=1}^R{r_i})!}{\prod_{i=1}^R{(r_i!)}}}) \, :\sum_{i=1}^{R}{i \cdot r_i}##

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# A Finding the bounds of a ratio

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