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     Russell doesn't really wish to say that two classes are similar if they are correlated. He needs a correlation which isn't a grossly material one, which in fact is the possibility of a material correlation. And that means that when he says A & B are 1-1 correlated it really means they can be, or it makes sense to say that they are.
     So we are driven to consider cases in which it makes sense & such in which it makes no sense to say that

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two classes are 1-1 correlated.
     What is the condition of their being 1-1 correlatable.