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.

>>30
I think he was trying to make the point that there's nothing to cite for doing such a thing. That you're essentially "making something up". Original research would be against the rules. However, Busy Beavers HAVE been nested, by Stephen Kleene in 1943.

BB(BB(n)) = BB₂(n)

Then of course you could do stuff like BB_BB(y)(x).