User:Vel/pu/Other things

Compounded exponential notation
This notation is in the form a[...] where [...] is an array of entries, each of which is either a number or a plus sign. An example of a valid expression is 10[+,1,2], which solves into the number time-plusoogol. The number outside of the array is called the base.

The rules are as follows:


 * [terminating rule] If the base is 1, set the expression to 1
 * [base rule] If the array is empty, set the expression to the base
 * [cropping rule] If the last entry in the array is 1, remove it
 * [recursive rule #1] If there are any plus signs in the array, then go to the first plus, and:
 * If the first plus is the first entry of the array, it is replaced with the expression but with the base decreased by one.
 * If the first plus is preceded by a one, set it to the base.
 * Otherwise, replace the plus with the expression but with the number before it decreased by 1.
 * [diagonalizing rule] If there are no pluses in the array and the first entry is one, decrease the first non-one entry by one, and replace all previous entries with pluses
 * [recursive rule #2] Otherwise, decrease the first entry and multiply by the base.

This should get us to $$\omega^{\omega}$$.

Numbers:


 * Dekgol = 10[10]
 * Lekgol = 10[50]
 * Googol = 10[100]
 * Demgol = 10[500]
 * Kilgol = 10[1000]
 * Myrgol = 10[10000]
 * Lakgol = 10[100000]
 * Meglogol = 10[1000000]