User blog comment:MilkyWay90/Help understand the zeta ordinals/@comment-5529393-20180620055127

For any \(\alpha\), \(\zeta_{\alpha} = \varepsilon_{\zeta_{\alpha}}\); this is the defining feature of the \(\zeta\) ordinals. In particular, \(\zeta_{\alpha}\) is the \(\alpha\)th ordinal that is fixed by the \(\varepsilon\) function, counting from 0.