There are ways to determine the relative size of numbers even when you cannot write down the digits. It's how we know TREE(3) is larger than Ackermann(20) (or maybe larger than any description of simple recursive uses of Ackermann using only Ackermann(20) symbols -- so even [It's Ackermann sub 6 applied Ackermann sub 5 times to Ackermann sub 5 and so on, where Ackermann sub 1 is the Ackermann function] doesn't get close). Notice that claim is strong enough it doesn't matter what number you start with. 20, 3, a googolplex. It's all basically the same size.
