# The busy beaver grows fast!

If $\Sigma$ denotes the busy beaver function, how can I then show, that there is an $t\in \mathbb{N}$ such that for all $x\geqslant t$ we have $\Sigma(x)>f(x)$, where $f$ is an arbitrary partial recursive function?

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The (even original) proof of the theorem can be found here on page 880.

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