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We can store as a list of (coeff, exponent) where exponent is another CNF ordinal.
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- ( \omega[n] = n )
- ( \omega^\alpha+1[n] = \omega^\alpha \cdot n )
- ( \omega^\lambda[n] = \omega^\lambda[n] ) for limit ( \lambda )
- Veblen: ( \varphi(0, \beta)[n] ) … standard rules
- Buchholz OCF: ( \psi_\nu(\alpha)[n] ) with explicit case distinctions
This reveals the complexity: manual step‑by‑step is tedious. A good calculator automates ordinal reduction and function iteration. fast growing hierarchy calculator high quality
