Does every common error in arithmetic and algebra have an error commutator? What happens when we cycle the data in an error commutator?
What about geometry? trig? analytic geometry? calculus?
For trig identities can we develop commutators for common errors?
How do error commutators relate to propagation of error analysis in numerical analysis?
How do error commutators relate to approximation theory in calculus?
Successor, predecessor, a given function applied to an input are unary operators.
In contrast, addition and multiplication are binary operators.
Project: What sort of error patterns are there for unary operators as opposed to binary operators?
Project: If we fix a value in a binary operator, we get a unary operator. What specific types of error commutators does that suggest?
Project: How do operator commutators compare to data commutators for teaching errors? What courses can operator commutators be used in? What courses can data commutators be used in?