# Optimal Classification/Rypka Method/Equations/Separatory/Characteristic/Theoretical

## Theoretical Separation

### The general identification equation

${\displaystyle S_{j}={\frac {1-{V^{-j}}}{1-V^{-C}}}}$, where:[1]
• Sj is the theoretical separatory value per jth characteristic,
• C is the number of characteristics in the group,
• V is the highest value of logic in the group and
• j is the jth characteristic index in the target set, where:
j = 0..K and where:
• K is the number of characteristics in the target set.

### Minimal number of characteristics to result in theoretical separation

${\displaystyle t_{min}={\frac {\log G}{\log V}}}$, where:[2]
• tmin is the minimal number of characteristics to result in theoretical separation,
• G is the number of elements in the bounded class and
• V is the highest value of logic in the group.

## Notes

1. See page 153, page 167, Fig. 2. & page 175 of the primary reference
2. See page 157, Primary Schemes footnote of the primary reference