User blog:Ecl1psed276/Introduction and Analysis of Star Notation - Part 1

Hey everyone, I'd like to introduce my new notation called Star Notation. This

Basics
The first rule of Star Notation is this: a[0]b = a+b. So 3[0]5 = 8, and 276[0]276 = 552. Then, we say that a[0][0]b = a[0]a[0]a[0]a....a[0]a (where there are b a's). Expressions like this are evaluted from right to left, so for example 4[0]5[0]6 = 4[0](5[0]6). It is fairly easy to see that a[0][0]b is equal to a*b, becuase we are just adding a to itself b times. The next step is to say a[0][0][0]b = a[0][0]a[0][0]a[0][0]a...a[0][0]a (where there are b a's). a[0][0][0]b is equivalent to exponentiation. Then of course we can say a[0][0][0][0]b = a[0][0][0]a[0][0][0]a...a[0][0][0]a (where there are b a's), and we can continue adding [0]'s for as long as we want. So here is what we have so far: a[0]b is addition, which has level 0 in the FGH. a[0][0]b is multiplication, which has level 1. a[0][0][0]b has level 2 (exponentiation), a[0][0][0][0]b has level 3 (tetration), etc. So the ordinal limit of our notation so far is \(\omega\).

Bracket Notation
COMING SOON!

Linear Array Notation
ALSO COMING SOON!