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  • B1mb0w

    The HyperRex Function

    April 29, 2018 by B1mb0w

    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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  • B1mb0w

    The Hyper Function

    April 28, 2018 by B1mb0w

    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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  • B1mb0w

    This blog will compare recursive functions such as Veblen and my own Big number and T-Rex 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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  • B1mb0w

    The Big number function

    April 10, 2018 by B1mb0w

    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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  • B1mb0w

    The Jurassic Number

    April 9, 2018 by B1mb0w

    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 T-Rex 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 T-Rex function to equal:

    \(T(1,0_{[n]},n) \approx f_{\vartheta(\Omega^{\omega^2.2})}(n)\)

    The Jurassic Number is equal to a T-Rex Function with 65,500,000 (65.5…






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