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If I understand correctly you two are saying that the infinity in the Chovos Halivavos is a form of infinity that encompasses the entire realm of existence and nonexistence. Therefore even if subtracting is just making a part become nonexistant it is still part of the whole. However, besides that this is hard to understand, if I explain the context of the CH I think it will become clear that this doesn’t answer the q.
When disproving the theory that the world has always existed and every person was born from parents going back forever without ever having someone who was the first person, the CH examines the ten generations between Noach and Avraham. This he says proves that the total generations ever is a finite number because there is no such thing as a part of infinity. To me this just seems like abstract math. Why can’t we give everyone a number and say that those aforementioned generations are 1- 10?