The biggest number

I have given you all an index card. You have one minute to write down the biggest number that you can (barring infinity) using any mathematical function that you know (addition, subtraction, exponentation, ackermann, Knuth's up arrow, etc). Go.

>>28
>While nested Busy Beavers seems a natural extension...

Wrong.

BB(x) grows faster than any computable function.  Therefore, since BB(x) ↑↑↑↑ BB(x) is computable (once you know BB(x)), BB(BB(x)) gets bigger faster than BB(x) ↑↑↑↑ BB(x).

What you could do, is go nuts and do something like

f1(n) = BB(BB(BB...n times...(BB(9)))...)))
f2(n) = f1(f1(f1...f1(n) times...(n))))...)))
f3(n) = f2(f2(f2...f2(n) times...(n))))...)))
etc.

You can probably do more than that even, but you get the idea.  I don't know enough about the BB() function to know whether it's possible in principle to actually find it's value given infinite time, though.