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Comment by tromp

6 months ago

> it makes other "googology" numbers vanish by comparison.

I consider TREE to be medium sized in the googology universe. It obliterates Graham's Number of course, as well as Goodstein sequence and simple hydras. But it's easily bested by an ingenious matrix generalization of hydras known as the Bashicu Matrix System, even when fixed at 2 rows. 3-row BMS goes far beyond that, let alone n-row. BMS is so simple that it can be encoded in under 50 bytes [1], where TREE would take significantly more. Beyond that there vastly greater numbers still such as Loader's Number. I shouldn't mention Rayo's because that's no longer computable in the usual sense.

[1] https://codegolf.stackexchange.com/questions/18028/largest-n...