I'm looking for an example of a complete definition of a custom calculus I could learn from to mathematically correct define my own calculus consinsting of:
- objects: a, aa, aaa, aaaa, aaaa, ... , b, bb, bbb, bbbb, etc
- operations on those objects: + , - , *; eg: a+a = aa
- etc...
Basically I want to remap natural numbers and the basic functions for my own needs and am looking for good resource to define a mathematically sound framework.