 The primitive recursive functions and relations encompass a broad class including virtually all those encountered in ordinary mathematics outside of logic or computability theory. This is illustrated in part by the fact that \(\mathbf{PR}\) contains functions such as \(supexp(x,y)\) which grow far faster than those whose values we can feasibly compute in practice in the sense studied in computational complexity theory. But the robustness of the class \(\mathbf{PR}\) is also attested to by the fact that its definition is invariant with respect to a variety of modifications—e.g., with respect to the classes of initial functions \(I_{\mathbf{PR}}\) and functionals \(Op_{\mathbf{PR}}\) on which its definition is based.