User:Ubersketch/A Guide

I wrote this page because most resources on Googology were unfinished or hard to understand. This might turn out to be ironic in the future but I'll start anyways.

Hyperoperations
You might be familiar with your basic arithmetic operations, addition, multiplication, and exponentiation. We will define addition later on but you only really need your current knowledge. Let's create an inductive definition.

a{0}b = a+b

a{b+1}c = a{b}a{b}a... with c amounts of a.

The first rule is self explanantory but the second rule may seem dubious to you, since it relies on itself for it's definition, which may make it seem circular. But it isn't. Eventually, you'll reach {0} which ends the cycle.

Now, this definition may not seem very useful, but it essentially continues the sequence addition, multiplication, and exponentiation. Remember in school, they taught you that multiplication is repeated addition, and repeated multiplication is exponentiation. If you were very observant, yu may realize that {1} is multiplication, and {2} is exponentiation. What goes after {2}? Tetration, pentation, hexation...

Bower's Exploding Array Function and Predecessors
The base is the first entry in the array.

The prime is the second entry in the array.

The pilot is the first non-1 entry after the prime.

The copilot is the entry right before the pilot.

The passengers are all the entries before the copilot.

If the prime is 1, then the value of the array is the base.

If there is no pilot, then the value of the array is the base to the power of the prime.

If the above rules don't apply then: An array looks like {a,b,c,d...}
 * 1) Pilot decreases by 1.
 * 2) Copilot takes on the value of the original array with the prime decreased by 1.
 * 3) Each passenger becomes the base.