But this is very misleading. What does “continue” mean? We have \(T_0\), \(T_1\), \(T_2\), …. None of these may be a fixed point. For instance, suppose we carry out this construction with the functional arising from \eqref{evenone} for \(\even(x)\). Then \(T_0\) will be \(\langle E_0, O_0\rangle\), where both \(E_0\) and \(O_0\) are the everywhere undefined 1-place relation. We leave it to you to check that we get successive \(T_i=\langle E_i, O_i\rangle\) where we have the following, with cases not displayed being undefined. 