User blog comment:MilkyWay90/Help understand the zeta ordinals/@comment-30869823-20180623115657

You already have some good answers but what helped me understand the veblen hierachy/fixed points was a definition for there fundamental sequence if you let \( f' \) be the function naming the fixed points of f

\( f'(\alpha)=\text{the $\alpha^th$ ordinal in } \{y|y=f(y)\}=\text{the $\alpha^th$ fixed point of } f \)

Than

\( f'(0)=\sup\{0,f(0),f^2(0),f^3(0),…\} \)

\( f'(\alpha+1)=\sup\{\alpha,f(\alpha),f^2(\alpha),f^3(\alpha),…\} \)

\( f'(\alpha)=\sup\{ f'(\alpha[n]), n \in \omega \} \)

if \( f(x)=\omega^x \) you get the ε-numbers. if \( f(x)=\epsilon_x \) you get the ζ-numbers.