<s>[INST] I think there's some confusion about the concept of "equality" in the sense of abstract algebra. You see, the algebraists who use the word "equality" are actually referring to what you folks would call "isomorphism". From a philosophical or metaphysical perspective, the word "equality" should only be used when things are actually the same. In my experience, however, algebraists don't seem to care about this, and I think it's due to a lack of philosophical background.  Am I right?[/INST]