Graham's number

Graham's number is one of the biggest numbers ever used in a constructive/practical way. It uses Knuth uparrow notation.
== Definition ==
Graham's number uses the G function, with G_{64} being Graham's number.
G_1 would be 3 \uparrow \uparrow \uparrow \uparrow 3. This number alone is ridiculously big, and is pretty much unimaginable. However, G_2 would be 3 \uparrow \cdots G_1 \cdots \uparrow 3. G_3 would be 3 \uparrow \cdots G_2 \cdots \uparrow 3, and so on until 3 \uparrow \cdots G_{63} \cdots \uparrow 3, which is G_{64}.
Graham's number can also be represented like this:
\left.
 \begin{matrix}
 G &=&3\underbrace{\uparrow \uparrow \cdots \cdots \cdots \cdots \cdots \uparrow}3 \\
 & &3\underbrace{\uparrow \uparrow \cdots \cdots \cdots \cdots \uparrow}3 \\
 & & \underbrace{\qquad \quad \vdots \qquad \quad} \\
 & &3\underbrace{\uparrow \uparrow \cdots \cdots \uparrow}3 \\
 & &3\uparrow \uparrow \uparrow \uparrow3
 \end{matrix}
\right \} \text{64 layers}
Category:Number