Graham's number is VASTLY less than TREE(3), so you lose, actually. Graham's number is around A(64)(4), i.e., the result of iterating the number of Knuth arrows 64 times starting with 4 Knuth arrows, while A(A(187196))(1) is an extremely weak lower bound on...
The maximum length of a sequence of labeled trees, with 3 labels, such that the Nth tree has at most N nodes and no tree can be embedded in any later tree... this being the definition of TREE(3).
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Graham's number is VASTLY less than TREE(3), so you lose, actually. Graham's number is around A(64)(4), i.e., the result of iterating the number of Knuth arrows 64 times starting with 4 Knuth arrows, while A(A(187196))(1) is an extremely weak lower bound on...
The maximum length of a sequence of labeled trees, with 3 labels, such that the Nth tree has at most N nodes and no tree can be embedded in any later tree... this being the definition of TREE(3).
See http://en.wikipedia.org/wiki/Kruskals_tree_theorem