# Graham's number

Graham’s number is a… rather large number. Letting $$f(x) = 3\uparrow^n 3$$ (in Knuth up arrow notation) and $$f^n(x) = \underbrace{f(f(f(\cdots f(f(x)) \cdots ))}_{n\text{ applications of }f}$$, Graham’s number is defined to be $$f^{64}(4).$$

The result is sizable. For an explanation of how large this is and why, see Tim Urban’s explanation at Wait but Why.

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