User blog:B1mb0w/The Quantum Function

The Quantum Function
My new Quantum function is the fastest growing function I have defined. The Quantum function is a set of two functions \(Q\) and \(t\) and has a growth rate well beyond \(f_{\vartheta(\Omega\uparrow\uparrow\omega)}(n)\)

Notation Explained
I use notation that is not in general use. For example parameter subscript brackets, leading zeros assumption, recursion parameter subscript \(*\), and the decremented function \(C\).

Refer to this blog for a complete explanation of this notation.

Defining the Quantum function
Here is an example of this notation being used to define the Veblen function.

\(O = \varphi(1) = \omega\)

\(\varphi(c + 1) = O^C\)

\(\varphi(1,c + 1) = C\uparrow\uparrow O\)

\(\varphi(1,0_{[y + 1]},c + 1) = \varphi^O(1,0_{[y]},C_*)\)

\(\varphi(a_{[x]},b + 1,c + 1) = \varphi^O(a_{[x]},b,C_*)\)

\(\varphi(1,0_{[z + 1]}) = \varphi^O(1_*,0_{[z]})\)

\(\varphi(a_{[x]},c + 1,0_{[z + 1]}) = \varphi^O(a_{[x]},c,0_*,0_{[z]})\)

Further References
Further references to relevant blogs can be found here: User:B1mb0w