Graham's number

[summary: Graham's number is a… rather large number. Tim Urban of Wait but Why gives a good introduction.

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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.