M2C2A: Episode 9, Goodbye Graham's number, you ain't big anymore.

What if we could make a number BIGGER than Graham's number, just for fun.
We'll call Graham's number G.
First of all, G+1.
Much more drastic, G*2.
Even greater, G^G. Or (G!)^(G!). 
But what if we invent some mathematical terms for a certainly bigger number, so, SO BIG, that by only writing the number of digits, of the NUMBER OF DIGITS, OF THE NUMBER OF DIGITS, YOU'D GET A NUMBER BIGGER THAN (((G!)!)!)!
How about we invent the "exponetorial"?
Let's write this as "¡".
This, instead of the factorial, which is 2*3*4*...n, goes 2^(3^(4^(5...n?))...)
So for example 2¡ would be 2,
3¡ would be 8,
4¡ would be 4,096,
5¡ would be 1,152,921,504,606,846,976, and
6¡ would be 2.3485425827738332278894805967893e+108!!! (the ! are exclamation signs).
7¡ would be 3.9408424552214162695348543183639e+758,
8¡ would be 5.8171811191842110297035069398346e+6068, and only
9¡ would be an overload for my 9.99999999999999999999999999999999e+9999 calculator!!!
How would we express G¡? And
(((((G¡)¡)¡)¡)¡)¡?!
Now, how about we try something definitively bigger than that.
Let's start with G¡. Now put G¡ "¡" after G (A.K.A G¡¡...¡¡¡, where the total number of "¡" is G¡). Let's call this G_1¡. 
Now let's make G_2¡ which will be G¡¡...¡¡¡, where the number of "¡" is now G_1¡. If you continue this to G_G¡, what will you get? An non-infinite number beyond what you could think possible!!!!! And G_G¡^G_G¡?! (Your brain can explode now).
-The Roaring Thunder