& 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}.
Category:Miner's Pages
Category:Math functions