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:

$$\left. \begin{matrix} G &=&3\underbrace{\uparrow \uparrow \cdots \cdots \cdots \cdots \cdots \uparrow}3 \\ & &3\underbrace{\uparrow \uparrow \cdots \cdots \cdots \cdots \uparrow}3 \\ & & \underbrace{\qquad \quad \vdots \qquad \quad} \\ & &3\underbrace{\uparrow \uparrow \cdots \cdots \uparrow}3 \\ & &3\uparrow \uparrow \uparrow \uparrow3 \end{matrix} \right \} \text{64 layers} $$