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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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  • B1mb0w

    The T-Rex Function

    April 8, 2018 by B1mb0w

    The T-Rex function generates very large numbers. It has a growth rate approaching \(f_{LVO}(n)\).

    The T-Rex Function is a family of functions \(T()\), \(r()\) and \(e()\) and \(x()\) which use this simple rule set:

    \(T(n) = T(0,n) = n + 1\)

    \(T(a + 1, n) = T^n(a,n_*)\)

    \(T(x(0), n) = T(n,n)\) and other instances of \(n\) can be substituted with \(x(0)\)

    \(x(a + 1) = T^{x(a)}(x(a)_*,x(a))\)

    and

    \(x(1, 0) = x^{x(0)}(0)\)

    \(x(1, a + 1) = x^{x(1, a)}(x(1, a))\)

    \(x(b + 1, 0) = x^{x(b, 0)}(b, 0_*)\)

    \(x(1, 0, 0) = x^{x(1, 0)}(1_*, 0)\)

    and

    \(e(0) = x(1, 0_{[x(0)]})\)

    \(e(a + 1) = T^{e(a)}(e(a)_*,e(a))\)

    \(e(1, 0) = e^{e(0)}(0)\)

    \(e(1, a + 1) = e^{e(1, a)}(e(1, a))\)

    \(e(b + 1, 0) = e^{e(b, 0)}(b, 0_*)\)

    \(e(1, 0, 0) = e^{e(1, 0)}(1_*, 0)\)

    and

    \(r(0) = e(1, 0_{[…


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  • B1mb0w

    The Rex Function

    April 8, 2018 by B1mb0w

    THIS BLOG HAS BEEN REPLACED BY MY BLOG ON The T-Rex Function WHICH IS MUCH STRONGER.

    The Rex function generates very large numbers. It has a growth rate approaching \(f_{LVO}(n)\).

    The Rex Function is a family of functions \(R()\), \(e()\) and \(x()\) which use this simple rule set:

    \(R(n) = R(0,n) = n + 1\)

    \(R(a + 1, n) = R^n(a,n_*)\)

    \(R(x(0), n) = R(n,n)\) and other instances of \(n\) can be substituted with \(x(0)\)

    \(x(a + 1) = R^{x(a)}(x(a)_*,x(a))\)

    and

    \(x(1, 0) = x^{x(0)}(0)\)

    \(x(1, a + 1) = x^{x(1, a)}(x(1, a))\)

    \(x(b + 1, 0) = x^{x(b, 0)}(b, 0_*)\)

    \(x(1, 0, 0) = x^{x(1, 0)}(1_*, 0)\)

    and

    \(e(0) = x(1, 0_{[x(0)]})\)

    \(e(a + 1) = R^{e(a)}(e(a)_*,e(a))\)

    \(e(1, 0) = e^{e(0)}(0)\)

    \(e(1, a + 1) = e^{e(1, a)}(e(1, a))\)

    \(e(b + 1, 0) = e^{e(b, 0)…


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  • B1mb0w

    The R Function

    March 4, 2018 by B1mb0w

    THIS BLOG HAS BEEN REPLACED BY MY BLOG ON The Rex Function WHICH IS MUCH STRONGER.

    The R function generates very large numbers. It is based on my earlier work on the The S Function.

    It has a growth rate \(\approx f_{LVO}(n)\).



    The R Function is actually two functions \(R()\) and \(r()\) which use this simple ruleset:

    \(R(n) = R(0,n) = n + 1\)

    \(R(a + 1, n) = R^n(a,n_*)\)

    \(R(r(0), n) = R(n,n)\) and other instances of \(n\) can be substituted with \(r(0)\)

    \(r(a + 1) = R^{r(a)}(r(a)_*,r(a))\)

    and

    \(r(1, 0) = r^{r(0)}(0)\)

    \(r(1, a + 1) = r^{r(1, a)}(r(1, a))\)

    \(r(b + 1, 0) = r^{r(b, 0)}(b, 0_*)\)

    \(r(1, 0, 0) = r^{r(1, 0)}(1_*, 0)\)

    and

    \(R(1, 0, n) = R(r(1, 0_{[r(0)]}),n)\)



    Some R Function identities are:

    \(R(R(R(a,b)),b) > R(R(a,b),R(a,b))\)

    because

    \(R(R…






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