 Why study entire classes? Well, consider for example the set \(Z\) of integers along with the binary operation of addition \(x+y\), the unary operation of negation \(-x\), and the constant 0. These operations and the constant satisfy various laws such as \(x+(y+z) = (x+y)+z, x+y = y+x, x+0 = x\), and \(x+(-x) = 0\). Now consider any other algebra with operations that not only have the same names but also satisfy the same laws (and possibly more), called a model of those laws. Such an algebra could serve any of the following purposes.