User blog:VoidSansXD/Alpha-Numeral notation

Alpha-Numeral Notation:
The alpha-numeral notation takes Ron Graham's Notation, and increases how big it is by.... well, alot. First, let's start with g(n). g(n) = 3(g(n-1) ↑'s)3. Also, G(1) is just 3↑↑↑↑3, or 3{4}3. Using this, we can create numbers even larger than Graham's number, just by adding one to the (n)!

Graham's number is just g(64), but let's go bigger. g(65) is ALREADY on a WHOLE NEW LEVEL of size, but then comes g(66). We can keep going like this for quite a while. Eventually, Knuth's up arrow notation is going to get involved in this. What happens when we get to g(g(1)), however? Well, g(g(1)) is just g(3↑↑↑↑3), or g(3{4}3). g(g(2)) is just g(3↑(g(1)↑'s)3). We can add more and more G's, But this eventually become's arbitrary. Once we get to g(g(g(g(g.......g(1))).....))) with g(1) g's, then we'll have to try something else.  Let's call this number h(g(1)).

How does this work, you ask? Well, h(n)= g(g(g(g...g(1)))....)))) With n g's.  For example, h(1) is just g(1) Since there's only one g.  h(2) is g(2) g's, etc.  Eventually, we'll reach h(h(h(h(h(h(h......h(1)))))....))))) with h(1) h's.Let's call THIS number I(h(1)). This works the same way as the h-system. I(n) = h(h(h(h(h(h(h...h(h(1)))......)))))) with n h's.  These letters continue until z, following the pattern.  Once we get to z(z(z(z(z....z(z(1)))).....)))))))) with z(1) z's, we have to label the numbers.  {n_(1)} = the n'th letter of the alphabet that is after g.  For example;  {8_(1)} = h(1).  Since the alphabet doesn't have infinite symbols, this is extremely useful.  Eventually, we'll reach {{8_(1)}_(1)}, then {{{8_(1)}_(1)}_(1)}, etc.  We'll have to use a new system for this.  {a_b(1)} = {{{{{...{{{{{n_(1)}_(1)}_(1)}.....(1)} with b 1's.  For example, {8_3(1)} =  {{{8_(1)}_(1)}_(1)}.  Eventually, we'll reach {8_-8_3(1)-(1)}, which is equal to {{8_{8_3(1)}(1)}.

W.I.P
Sorry about not finishing my notation, it's stil a work in progress. This notation will be added on later.