Counting in Wonderland

You know what you do if you have an interest in math? You make up you're way to count. Be warned, this is not for the faint of heart.

I have to say counting in decimal isn't much fun. A lot of you may know how to count in binary, some of you may know something like hexadecimal or octal, and the true power nerds may know something obscure like Mayan counting or Babylonian. What's more fun than trying to count in these already established systems? Making up our own and learning the process as we go along.
When I was wee little lad, I used to enjoy learning code and making up my own to share with my friends. Of course, when you're young, your codes are nothing more than swapping one letter for another. That's how we'll start today, by using the symbols of the alphabet to represent numbers. The first letter and number in our counting system will be A. A will not represent the singular. A will be nothing. If we say we have A of something, then we have none of it. This might be confusing to some, but the idea of having nothing represented symbolically is an old idea that is fairly useful, to put it lightly. If I have a singular orange, then I'll have B orange. If I place B orange down, then the result is C.  D is B more than C. Now we can continue to extend this logic Z, which is B more then Y, C more than X, and W  more than D.
What comes after Z? This is a number far from infinity, you will hopefully reach an age older than Z, and I hope you will have way more money than Z. It may do for a silly paper on math, but for everyday use, it's useless.
Let us go back to A. In roman numerals, you change the sign at significant numbers to reduce the amount of  "I"s you have to draw. I can't add signs, but I can add rules! Mwahahahahaha. The first spot, you multiply the number by B. If you add another spot, BA, that B is now equal to BA = Z + B. We can now call that the "BA" spot. And you can extend it further, BAA, is equal to ZZ + B. You can do this for as many numbers as you like. As you extend the spots, any place will be equal to (Z + B) ^Ж where Ж is the number of characters. For example, (Z + B)^G would be BAAAAA. (Z + B)^J would be BAAAAAAAA. BB is B more than BA. CA is (Z + B) * C. CB is B more than CA, and CZ is Z more than CA and is B less than DA.
We can create a decimal point by using division. A.B  is equal to B/BA. A.AB = B/BAA. And logically this can be extended outwards.
This is probably confusing and silly to most people. Quite honestly, I've been reading about Lewis Carrol recently, so this in part is inspired by him. Also, this was an old puzzle I used to post to dating sites when I got bored, and I decided it was time to bring it out. What I really want to work on with it though, is how math works within this set. This uses basic logic to set up rules. After reading a book about quaternions, I was curious how to set up a mathematical system based on any other system of logic. That essay will be coming at some point, but for now I'll set up the numbers first.
Enjoy this alphadecimal system.  Feel free to play with it a little, and post and questions or comments below.