& 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 $$4 \overset{x}{\&} = Ma_{x+1}$$.