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# B1mb0w

My favorite wikis
• ## 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(… Read more > • ## 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…

• ## 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_{[… Read more > • ## 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)… Read more > • ## 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…