& function

The & function ($x\overset{y}{\&}$) is a very rapidly growing function. It is a shortening of MBN's [x,x].

It works like this:

1& = [1,1] = 1↑1 = 1

2& = [2,2] = 2↑↑2 = 4

3& = [3,3] = 3↑↑↑3 = $\underbrace{3^{3^{\cdots^{3^3}}}}_{\approx 7.6*10^{12}}$

4& = [4,4] = 4↑↑↑↑4 = Ma₂

...

But then, you could NeSt It LoL xD

So, x& is always $x \overset{1}{\&}$, but when you want to indicate multiple &'s, then you use $\overset{y}{\&}$ (ex: $5 \overset{3}{\&} = 5 \& \& \&$). The & function with the number on top being 2 can be expressed as [[x,x],[x,x]], and the number of the top being 3, it will be [[[x,x],[x,x]],[[x,x],[x,x]]], and the number in the top being 4, then the MBN will be [[[[x,x],[x,x]],[[x,x],[x,x]]],[[[x,x],[x,x]],[[x,x],[x,x]]]], and so on.

Another cool fact is that $4 \overset{x}{\&} = Ma_{x+1}$.