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Branch of combinatorics with the philosophy that 'total disorder is impossible'. For example, Ramsey's theorem asserts that for each $n$, every sufficiently large graph either contains a clique of size $n$ or a stable set of size $n$.
4
votes
Magnitude of Graham's Number?
Here's one way to put it:
3↑↑3 = 3^(3^3) ~= 7.6 trillion
3↑↑↑3 = 3↑↑(3↑↑3) = 3↑↑(7.6 trillion). Let's start calculating this number:
3↑↑4 = 3^(7.6 trillion) ~= 10^(3.6 trillion) > a google
3↑↑5 = …