User blog:KthulhuHimself/Almanac Notation

Another function.

Rules
For starters, redefine: 10^^0 = 1

 Then:

0 ₳b = (b+1) ₳0 ₳(b-1)

a₳0 = 10^^a

a ₳1 = (a+1) ₳ (a-1)

a ₳b = (((((a-1) ₳b) ₳b ) ₳b... ) ₳b) ₳b (b nests)

These are to be solved from left to right.

examples
 1 ₳0 = 10

 0 ₳1 = 0 ₳0 ₳0 = 1 ₳0 = 10

0 ₳2 = 3 ₳0 ₳1 = (10^^3) ₳1 = ((10^^3)-1) ₳ ((10^^3)-1)

Conclusion
I have a feeling this notation is extremely powerful, yet can not be sure wherever it will ever even resolve.