User blog:Ynought/My attempt at an ordinal function

An attempt at an ordinal function
\(\eta\) is anything it could even mean that an alpha after it is in a power tower or in another function or in a subscript

\(\Theta(0)[n]=n\) and \(\Theta_0=\Theta\) here \(\alpha[n]\) is the n-th term in the fundamental sequence of \(\alpha\)

\(\Theta(\eta\alpha)[n]=\Theta(\eta\alpha[n])\) Limit case

\(\Theta(\eta\alpha+1)[n]=\Theta(\eta\alpha)\uparrow\uparrow n\) n times

\(\Theta(\eta\Omega)=sup(\Theta(\eta\omega),\Theta(\eta\omega+\Theta(\eta\omega)),\Theta(\eta\omega+\Theta(\eta\omega+\Theta(\eta\omega)))),...)\)

\(\eta\Omega_0=\eta\Omega\) and \(\eta\Omega_{\alpha+1}[n]=\eta\Omega_\alpha^{\dots^{\eta\Omega_\alpha}}​\) or \(\eta\Omega_\alpha\uparrow\uparrow n\)

to be continued