 The addition function \(\textit{add}(x,y)\) may, for instance, be defined in this way by taking \(f(x_0) = x_0\) and \(g(x_0,x_1) = s(x_1)\). This definition can also be thought of as specifying that the sum \(x+y\) is the value obtained by iterating the application of the successor function \(y\) times starting from the initial value \(x\) in the manner of (\ref{prex1}). Similarly, \(\textit{mult}(x,y)\) may be defined by taking \(f(x_0) = 0\) and \(g(x_0,x_1) = add(x_0,x_1)\). This defines the product \(x \times y\) as the value obtained by iterating the function which adds \(x\) to its argument \(y\) times starting from the initial value 0.