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posted by dennisn on October 13th, 2010 at 2:18PM
Graham's number, for one, "is an upper bound on the solution to a certain problem [1] in Ramsey theory." http://en.wikipedia.org/w...raham%27s_number
[1] Consider an n-dimensional hypercube, and connect each pair of vertices to obtain a complete graph on 2^n vertices. Then colour each of the edges of this graph either red or blue. What is the smallest value of n for which every such colouring contains at least one single-coloured 4-vertex planar complete subgraph? Googol(plex) aren't too useful, besides descriptively. (A googol is "astronomical", a googolplex is hyper-mega astronomical, etc.)
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