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Madore's $$\psi$$ function is a function for expressing extremely large countable ordinals.

## Defination

Madore's $$\psi$$ function is defined as follows:

$$S=\{0,1,\omega,\Omega\}$$ is our tool box.

$$C(0)=$$all of the things you can make from S and finite applications of $$+\times$$^ in S.

$$C(n+1)=$$ all of the things you can make from $$C(n)$$ and finite applications of $$+\times$$^$$\psi$$ in $$C(n)$$.

$$\psi(n)=$$ the first countable ordinal not in $$C(n)$$.

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