User blog comment:MilkyWay90/Trying to create my own ordinal notation/@comment-30869823-20180704210111/@comment-31966679-20180705182939

\(\varepsilon_{0} = \omega ^ {\varepsilon_{0}}\)

\(\varepsilon_{0} = lvl(3, \omega, \varepsilon_{0})\)

\(\varepsilon_{0} = \underbrace{lvl(3, \omega, lvl(3, \omega, lvl(3, \omega, lvl(\ldots))))}_\omega\)

\(\varepsilon_{0} = lvl(4, \omega, \omega)\)

\(\varepsilon_{1} = \varepsilon_{0} ^ \varepsilon_{1}\)

\(\varepsilon_{1} = lvl(3, \varepsilon_{0}, \varepsilon_{1})\)

\(\varepsilon_{1} = \underbrace{lvl(3, \varepsilon_{0}, lvl(3, \varepsilon_{0}, lvl(\ldots))))}_{\omega}\)

\(\varepsilon_{1} = lvl(4, \varepsilon_{0}, \omega)\)

\(\varepsilon_{n} = \varepsilon_{n - 1}^{\varepsilon_{n}}\)

\(\varepsilon_{n} = lvl(3, \varepsilon_{n - 1}, \varepsilon_{n})\)

\(\varepsilon_{n} = \underbrace{lvl(3, \varepsilon_{n - 1}, lvl(3, \varepsilon_{n - 1}, lvl(\ldots)))}_{\omega}\)

\(\varepsilon_{n} = lvl(4, \varepsilon_{n - 1}, \omega)\)

\(\varepsilon_{\varepsilon_{0}} = lvl(3, \varepsilon_{\varepsilon_{0}}, \varepsilon_{\varepsilon_{0}})\)

\(\varepsilon_{\varepsilon_{0}} = lvl(4, \varepsilon_{\varepsilon_{0}}, \omega)\)

\(\varepsilon_{\varepsilon_{0}} = lvl(3, \varepsilon_{\varepsilon_{0}}, \varepsilon_{\varepsilon_{0}}\)

\(\varepsilon_{\varepsilon_{0}} = lvl(4, \varepsilon_{\varepsilon_{0}}, \omega)\)

\(\varepsilon_{\varepsilon_{0}} = \underbrace{lvl(4, lvl(4, lvl(4, \ldots, \omega), \omega), \omega)}_{\omega}\)

\(\varepsilon_{\varepsilon_{\varepsilon_{0}}} = lvl(4, \varepsilon_{\varepsilon_{\varepsilon_{0}}}, \omega)\)

\(\varepsilon_{\varepsilon_{\varepsilon_{0}}} = lvl(4, \varepsilon_{\underbrace{lvl(4, lvl(4, lvl(4, \ldots, \omega), \omega), \omega)}_{\omega}}, \omega)\)

How do I get past this fixed point?