Well, the Hyperreals are a field. Then every element, including infinitesimals, must have an additive inverse. EDIT: That means pure Infinitesimals, i.e., those with Real part =0, must have an additive inverse.
I'm not aware of any probabilistic classifier. Usually you just compare the predicted with the actual known value/class of elements in the Testing set., all, like you said, given a threshold, so that, e.g., a threshold of 0.6 will give us a given Confusion Matrix Can you give us examples of...