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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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The Big number function is a very fast growing function. It's growth rate is well beyond \(f_{LVO}(n)\).
The Big number function is a pair of functions \(B()\) and \(g()\) which use this simple rule set:
\(B(n) = B(0,n) = n + 1\)
\(B(a + 1, n) = B^n(a,n_*)\)
\(B(g(0), n) = B(n,n)\) and other instances of \(n\) can be substituted with \(g(0)\)
\(g(c + 1) = g(0, c + 1) = B^{g(c)}(g(c)_*,g(c))\)
and
\(g(1, 0_{[d + 1]}) = g^{g(1, 0_{[d]})}(1_*, 0_{[d]})\)
\(g(b + 1, 0) = g^{g(b,0)}(b,0_*)\)
\(g(b, c + 1) = B^{g(b,c)}(g(b,c)_*,g(b,c))\)
and
\(g() = g_0()\)
\(g_{a + 1}(0) = g_a(1, 0_{[g_a(0)]})\)
\(g_a(c + 1) = B^{g_a(c)}(g_a(c)_*,g_a(c))\)
\(g_a(b + 1, 0) = g_a^{g_a(b,0)}(b,0_*)\)
\(g_a(b, c + 1) = B^{g_a(b,c)}(g_a(b,c)_*,g_a(b,c))\)
\(g_a(1, 0, 0) = g_a^{g_a(…
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The Jurassic Number is one of the largest named numbers. I calculate it is \(\approx f_{\vartheta(\Omega^{\omega^2.2})}(65500000)\).
It is calculated using the Jurassic Function \(Jurassic(n)\).
The Jurassic Function is defined using The TRex Function and this simple definition:
\(Jurassic(n) = T(1,0_{[n]},n)\) using parameter subscript brackets \([n]\).
Parameter subscript brackets are useful for functions with many parameters, such as:
\(M(a,0_{[1]}) = M(a,0)\)
\(M(a,0_{[3]}) = M(a,0,0,0)\)
\(M(a,b_{[2]}) = M(a,b_1,b_2)\)
\(M(a,0_{[2]},b_{[3]},1) = M(a,0,0,b_1,b_2,b_3,1)\)
I calculate this TRex function to equal:
\(T(1,0_{[n]},n) \approx f_{\vartheta(\Omega^{\omega^2.2})}(n)\)
The Jurassic Number is equal to a TRex Function with 65,500,000 (65.5…
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