Or like saying they should start their study of addition and multiplication from the perspective of group theory - since the integers (Z) under addition forms a

Or like saying they should start their study of addition and multiplication from the perspective of group theory - since the integers (Z) under addition forms a group because it satisfies closure, associativity, identity, and inverses, while Z under multiplication does not form a group because, although it satisfies closure, associativity, and identity, it fails to provide inverses for all elements.