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The Q-supersystem is a googological function by Wiki user Boboris02. It is a notation based on recursion and is very similar to many hierarchies.

## Basics

The Q-supersystem is a system that follows a very simple fundamental rule and that is:

$$Q_n(a)$$ is always at the next notation after $$Q_{n-1}(a)$$.

It also always accounts that $$Q_{n,0\#}(a)=Q_{n-1,a\#}(a)$$ no matter how much $$a$$ is.

Whenever you have more than one zeros like in this example $$Q_{1,0,0,...,0}(n)$$ then it can be simplified like so $$Q_{1,0,0,...,0}(n)=Q_{n,0,0,...,0}(n)$$ where now the number of zeros is reduced by 1 and the first entry becomes the number,the operation is done on.

Also, the first number must always be reduced by one. $$Q_{n,0,0,...,0}(a)=Q_{n-1,a,0,0...0,0}(a)$$

Whenever things like $$Q_{n,0\#,b}(a)$$ occur, it can be simplified through the following equation:

$$Q_{n,0\#,b}(a)=Q^{a}_{n,0\#,b-1}(a) \leadsto Q_{n,0\#,0}(c)=Q_{n-1,c,0(\#-1),0}(c)$$.

When there is only one entry, $$Q_0(n)=n+1,Q_1(n)=n2,Q_2(n)=n^2$$ and $$Q_{a+2}(n)=n\uparrow^a n$$ for $$n\geq 1$$.

The limit of the Q-supersystem ($$Q_{1,0,0,...,0,0}(n)$$) is approximately $$f_{\omega^{\omega}}(n)$$ in the FGH.

## Sources

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