 Veblen extended this idea first to arbitrary finite numbers of arguments, but then also to transfinite numbers of arguments, with the proviso that in, for example \(\Phi_{f} ( \alpha_{0} , \alpha_{1} , \ldots , \alpha_{\eta} )\), only a finite number of the arguments \(\alpha_{\nu}\) may be non-zero. Finally, Veblen singled out the ordinal \(E(0)\), where \(E(0)\) is the least ordinal \(\delta &gt; 0\) which cannot be named in terms of functions \(\Phi_{\ell} ( \alpha_{0} , \alpha_{1} , \ldots , \alpha_{\eta} )\) with \(\eta &lt; \delta\), and each \(\alpha_{ \gamma } &lt; \delta\).