Roughly speaking, a googolplex is doubly-exponentially huge, 3^^^^3 involves tetration, Graham's number is in a class of its own, and SSCG(3) even further beyond that.2nd question: if not, is it smaller than a googolplex?
3rd question: if not, it is smaller than?
4rd question: if not, is it smaller than Graham's Number?
5th question: it is smaller than SSCG(3)?
I'm already preparing for bigger cubes!Roughly speaking, a googolplex is doubly-exponentially huge, 3^^^^3 involves tetration, Graham's number is in a class of its own, and SSCG(3) even further beyond that.
Graham's number and SSCG(k) both come from graph theory, and their mindboggling size comes from the fact that many advanced combinatoric results cannot be proven in Peano arithmetic, which "contains", among other things, the class of easily computable functions. (Very roughly speaking.) These results require more axioms to prove than just Peano arithmetic (e.g. the standard set theory axioms: ZFC), and consequently, the functions that come out of such results have to grow extremely quickly. (If they didn't, Peano arithmetic would've been able to handle them… roughly speaking. It might be possible that such functions don't grow quickly, but the fact that they don't grow quickly cannot be proven in PA; I can't think of any such example, however.)
In contrast, if you're just looking at something like the number of states on an n×n×n cube, that's only singly-exponentially large. You shouldn't even expect it to hit a googolplex for reasonable values of n, much less Graham's number or SSCG(3).
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