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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 \(f_{\vartheta(\Omega\uparrow\uparrow\omega)}(n)\)
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.
Using my notation to define the \(Q\) function.
\(Q(c) = c + 1\)
\(Q(a_{[x]},c + 1,n) = Q^C(a_{[x]},c,n_*)\)
\(Q(1,0_{[c + 1]},n) = Q(t_C(0),0_{[c]},n)\)
\(Q(a_{[x]},c + 1,0_{[z + 1]},n) = Q(a_{[x]},c,t_C(0),0_{[z]},n)\)
Note that \(C\) is defined in my blog on notation.
Using my notat…
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I use notation that is not in general use, but I find very helpful to describe recursive functions. You will see this notation in use on my blogs. This blog will present the exact definition I intend for these notations. Any deviance from the notation here is most likely due to an error in one of my other blogs.
They notations are parameter subscript brackets, leading zeros assumption, recursion parameter subscript \(*\), and the decremented function \(C\).
\(M(a,0_{[2]}) = M(a,0,0)\)
\(M(a,0_{[2]},b_{[3]},1) = M(a,0,0,b_1,b_2,b_3,1)\)
\(M(0_{[x]},0_{[2]},b_{[3]},1) = M(0_{[x + 2]},b_1,b_2,b_3,1) = M(b_1,b_2,b_3,1)\)
\(M^2(a) = M^2(a_*) = M(M(a))\) and \(M(a,b_*) = M(a,b)\)
\(M^2(a,b_*) = M(a,M(a,b))\)
\(M^2(a_*,b) = M(M(a,b),b)\)
For any function…
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My new HyperRex function is compared here to recursive functions such as Veblen and my previous Hyper function. The HyperRex function is a set of two functions \(H()\) and \(r()\) and has a growth rate well beyond \(f_{\vartheta(\Omega\uparrow\uparrow\omega)}(n)\)
The notation I use here is not in general use, but I find helpful. They are parameter subscript brackets, leading zeros assumption, recursion parameter subscript \(*\), and the decremented function \(C\).
Parameter Subscript Brackets, where:
\(M(a,0_{[2]}) = M(a,0,0)\)
\(M(a,0_{[2]},b_{[3]},1) = M(a,0,0,b_1,b_2,b_3,1)\)
Leading Zeros Assumption, where:
\(M(0_{[x]},0_{[2]},b_{[3]},1) = = M(0_{[x + 2]},b_1,b_2,b_3,1) = M(b_1,b_2,b_3,1)\)
Recursion Parameter Subscript \(*\), where:
\(M^2(a)…
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This blog will compare recursive functions such as Veblen to my new Hyper function. The Hyper function is a set of two functions \(H()\) and \(p()\) and has a growth rate \(\approx f_{\vartheta(\Omega\uparrow\uparrow\omega)}(n)\)
The notation I use here is not in general use, but I find helpful. They are parameter subscript brackets, leading zeros assumption, recursion parameter subscript \(*\), and the decremented function \(C\).
Parameter Subscript Brackets, where:
\(M(a,0_{[2]}) = M(a,0,0)\)
\(M(a,0_{[2]},b_{[3]},1) = M(a,0,0,b_1,b_2,b_3,1)\)
Leading Zeros Assumption, where:
\(M(0_{[x]},0_{[2]},b_{[3]},1) = M(b_1,b_2,b_3,1)\)
Recursion Parameter Subscript \(*\), where:
\(M^2(a) = M^2(a_*) = M(M(a))\) and \(M(a,b_*) = M(a,b)\)
\(M^2(a,b_*) = M(a,…
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This blog will compare recursive functions such as Veblen and my own Big number and TRex functions.
The notation I use here is not in general use, but I find helpful. They are parameter subscript brackets, leading zeros assumption, recursion parameter subscript \(*\), and the decremented function \(C\).
Parameter Subscript Brackets, where:
\(M(a,0_{[2]}) = M(a,0,0)\)
\(M(a,0_{[2]},b_{[3]},1) = M(a,0,0,b_1,b_2,b_3,1)\)
Leading Zeros Assumption, where:
\(M(0_{[x]},0_{[2]},b_{[3]},1) = M(b_1,b_2,b_3,1)\)
Recursion Parameter Subscript \(*\), where:
\(M^2(a) = M^2(a_*) = M(M(a))\) and \(M(a,b_*) = M(a,b)\)
\(M^2(a,b_*) = M(a,M(a,b))\)
\(M^2(a_*,b) = M(M(a,b),b)\)
Decremented Function \(C\), where for any function:
\(M(a_{[b]},c + 1,d_{[e]})\) then \(C = M…
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