FANDOM


The g function is a function I coined myself. Not to be confused with the Graham Function or the Ultimate Googol Function or Joyce's g function.

Basic Definition

g_0(n) = 10^n

g_1(0) = g_0(100)

g_1(1) = g_0(g_0(100))

g_1(n) = g_0(g_1(n-1))

g_2(0) = g_1(100)

g_2(n) = g_1(g_2(n-1))

g_m(0) = g_(m-1)(100)

g_m(n) = g_(m-1)(g_m(n-1))

Pretty easy, eh?

Extensions

2 entry arrays

We define 2 entry arrays:

g_0,1(0) = g_100(100)

g_0,1(1) = g_(g_100(100))(100)

g_0,1(n) = g_(g_0,1(n-1))(100)

g_1,1(0) = g_0,1(100)

g_1,1(1) = g_0,1(g_0,1(100))

g_1,1(n) = g_0,1(g_1,1(n-1))

g_2,1(0) = g_1,1(100)

g_2,1(n) = g_1,1(g_2,1(n-1))

g_m,1(0) = g_(m-1),1(100)

g_m,1(n) = g_(m-1),1(g_m,1(n-1))

g_0,2(0) = g_100,1(100)

g_0,2(1) = g_(g_100,1(100)),1(100)

g_0,2(n) = g_(g_0,2(n-1)),1(100)

g_1,2(0) = g_0,2(100)

g_1,2(n) = g_0,2(g_1,2(n-1))

g_2,2(0) = g_1,2(100)

g_2,2(n) = g_1,2(g_2,2(n-1))

g_m,2(0) = g_(m-1),2(100)

g_m,2(n) = g_(m-1),2(g_m(n-1))

g_0,x(0) = g_100,(x-1)(100)

g_0,x(n) = g_(g_0,x(n-1)),(x-1)(100)

g_1,x(0) = g_0,x(100)

g_1,x(n) = g_0,x(g_1,x(n-1))

g_m,x(0) = g_(m-1),x(100)

g_m,x(n) = g_(m-1),x(g_m,x(n-1))

3 entry arrays

We define 3-entry Arrays:

g_0,0,1(0) = g_0,100(100)

g_0,0,1(n) = g_0,(g_0,0,1(n-1))(100)

g_1,0,1(0) = g_0,0,1(100)

g_1,0,1(n) = g_0,0,1(g_1,0,1(n-1))

g_m,0,1(0) = g_(m-1),0,1(100)

g_m,0,1(n) = g_(m-1),0,1(g_m,0,1(n-1))

g_0,1,1(0) = g_100,0,1(100)

g_0,1,1(n) = g_(g_0,1,1(n-1)),0,1(100)

g_1,1,1(0) = g_0,1,1(100)

g_1,1,1(n) = g_0,1,1(g_1,1,1(n-1))

g_m,1,1(0) = g_(m-1),1,1(100)

g_m,1,1(n) = g_(m-1),1,1(g_m,1,1(n-1))

g_0,x,1(0) = g_100,(x-1),1(100)

g_0,x,1(n) = g_(g_0,x,1(n-1)),(x-1),1(100)

g_1,x,1(0) = g_0,x,1(100)

g_1,x,1(n) = g_0,x,1(g_1,x,1(n-1))

g_m,x,1(0) = g_(m-1),x,1(100)

g_m,x,1(n) = g_(m-1),x,1(g_m,x,1(n-1))

g_0,0,2(0) = g_0,100,1(100)

g_0,0,2(n) = g_0,(g_0,0,2(n-1)),1(100)

...

g_0,0,y(0) = g_0,100,(y-1)(100)

...

g_m,x,y(0) = g_(m-1),x,y(100)

g_m,x,y(n) = g_(m-1),x,y(g_m,x,y(n-1))

Multiple Entry Array

We can define multiple entry arrays:

g_0,0,0,1(0) = g_0,0,100(100)

g_0,0,0,1(n) = g_0,0,(g_0,0,0,1(n-1))(100)

g_1,0,0,1(0) = g_0,0,0,1(100)

g_1,0,0,1(n) = g_0,0,0,1(g_1,0,0,1(n-1))

...

g_0,1,0,1(0) = g_100,0,0,1(100)

g_0,1,0,1(n) = g_(g_0,1,0,1(n-1)),0,0,1(100)

g_1,1,0,1(0) = g_0,1,0,1(100)

g_1,1,0,1(n) = g_0,1,0,1(g_1,1,0,1(n-1))

...

g_0,0,1,1(0) = g_0,100,0,1(100)

g_0,0,1,1(n) = g_0,(g_0,0,1,1(n-1)),0,1(100)

g_1,0,1,1(0) = g_0,0,1,1(100)

g_1,0,1,1(n) = g_0,0,1,1(g_1,0,1,1(n-1))

...

g_0,1,1,1(0) = g_100,0,1,1(100)

g_0,1,1,1(n) = g_(g_0,1,1,1(n-1)),0,1,1

g_1,1,1,1(0) = g_0,1,1,1(100)

g_1,1,1,1(n) = g_0,1,1,1(g_1,1,1,1(n-1))

...

g_0,0,0,2(0) = g_0,0,100,1(100)

g_0,0,0,2(n) = g_0,0,(g_0,0,0,2(n-1)),1(100)

...

g_0,0,0,0,1(0) = g_0,0,0,100(100)

g_0,0,0,0,1(n) = g_0,0,0,(g_0,0,0,0,1(n-1))(100)

...

g_0,0,0,0,0,1(0) = g_0,0,0,0,100(100)

g_0,0,0,0,0,1(n) = g_0,0,0,0,(g_0,0,0,0,0,1(n-1))(100)

...

g_0,0,0,...,0,0,1(0) = g_0,0,0,...,0,100(100)

g_0,0,0,...,0,0,1(n) = g_0,0,0,...,0,(g_0,0,0,...,0,0,1(n-1))(100)

Two row arrays

We define 2 row arrays:

g_0(1)1(0) = g_0,0,0,...,0,0,1(100) w/ 100 entries

g_0(1)1(n) = g_0,0,0,...,0,0,1(100) w/ g_0(1)1(n-1) entries

g_1(1)1(0) = g_0(1)1(100)

g_1(1)1(n) = g_0(1)1(g_1(1)1(n-1))

...

g_0,1(1)1(0) = g_100(1)1(100)

g_0,1(1)1(n) = g_(g_0,1(1)1(n-1))(1)1(100)

g_1,1(1)1(0) = g_0,1(1)1(100)

g_1,1(1)1(n) = g_0,1(1)1(g_1,1(1)1(n-1))

...

g_0,0,1(1)1(0) = g_0,100(1)1(100)

g_0,0,1(1)1(n) = g_0,(g_0,0,1(1)1(n-1))(1)1(100)

g_1,0,1(1)1(0) = g_0,0,1(1)1(100)

g_1,0,1(1)1(n) = g_0,0,1(1)1(g_1,0,1(1)1(n-1))

...

g_0,1,1(1)1(0) = g_100,0,1(1)1(100)

g_0,1,1(1)1(n) = g_(g_0,1,1(1)1(n-1)),0,1(1)1(100)

g_1,1,1(1)1(0) = g_0,1,1(1)1(100)

g_1,1,1(1)1(n) = g_0,1,1(1)1(g_1,1,1(1)1(n-1))

...

g_0,0,0,1(1)1(0) = g_0,0,100(1)1(100)

g_0,0,0,1(1)1(n) = g_0,0,(g_0,0,0,1(1)1(n-1))(1)1(100)

...

g_0,0,0,...,0,0,1(1)1(0) = g_0,0,0,...,0,100(1)1(100)

g_0,0,0,...,0,0,1(1)1(n) = g_0,0,0,...,0,(g_0,0,0,...,0,0,1(1)1(n-1))(1)1(100)

...

g_0(1)2(0) = g_0,0,0,...,0,0,1(1)1(100) w/ 100 entries

g_0(1)2(n) = g_0,0,0,...,0,0,1(1)1(100) w/ g_0(1)2(n-1) entries

-- Under Construction --

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