Reaching Towards The Infinite

In this section of Impossible Numbers I will show my attempt at creating the largest number currently in Googology. I started my journey with an question:  What if there was a function that made new functions?  And this  is how I did it:  First I came up with an axiom called: The axiom of functions, the axiom states that there is always a more powerful function with no relation  to previous functions.  So I created a function based off of the axiom here it is: EF(n) (EF stands for Extended Function).  Here is my definition for the EF function:  EF(1) is defined as 1^1 now EF(2) is the first function that much more powerful than the function used in EF(1) that can be defined without explaining the function used in EF(1) where all inputs = 2 so this function is the TREE function and the number is TREE(2) or just 2. Now  we can define that EF(3) is the first function that much more powerful than the function used in EF(2) that can be defined without explaining the function used in EF(1) and EF(2) where all inputs = 3 so its SSCG(3). Now as you can see this function is very powerful and can go far beyond the largest numbers in Googology. The next thing I will define is EFa(n).